Month

A month is a unit of time, used with calendars, which is approximately as long as a natural period related to the motion of the Moon; "month" and "Moon" are cognates. The traditional concept arose with the cycle of Moon phases; such months (lunations) are synodic months and last approximately 29.53 days. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moon's phases as early as the Paleolithic age. Synodic months, based on the Moon's orbital period with respect to the Earth-Sun line, are still the basis of many calendars today, and are used to divide the year. 
Types of months in astronomy.
The following types of months are mainly of significance in astronomy, most of them (but not the distinction between sidereal and tropical months) first recognized in Babylonian lunar astronomy.
A synodic month is longer than a sidereal month because the Earth-Moon system is orbiting the Sun in the same direction as the Moon is orbiting the Earth. The Sun moves eastward with respect to the stars (as does the Moon) and it takes about 2.2 days longer for the Moon to return to the same apparent position with respect to the Sun.
An anomalistic month is longer than a sidereal month because the perigee moves in the same direction as the Moon is orbiting the Earth, one revolution in nine years. Therefore, the Moon takes a little longer to return to perigee than to return to the same star.
A draconic month is shorter than a sidereal month because the nodes move in the opposite direction as the Moon is orbiting the Earth, one revolution in 18.6 years. Therefore, the Moon returns to the same node slightly earlier than it returns to the same star.
Calendrical consequences.
At the simplest level, most well-known lunar calendars are based on the initial approximation that 2 lunations last 59 solar days: a 30-day full month followed by a 29-day hollow month—but this is only roughly accurate and eventually needs intercalation (correction). Additionally, the synodic month does not fit easily into the solar (or 'tropical') year, which makes accurate, rule-based 'lunisolar' calendars complicated. The most common solution to this problem is the Metonic cycle, which takes advantage of the fact that 235 lunations are approximately 19 tropical years (which add up to not quite 6,940 days). However, a Metonic calendar will drift against the seasons by about one day every 200 years. Metonic calendars include the calendar used in the Antikythera Mechanism about 2,000 years ago, and the Hebrew calendar.
The complexity required in an accurate lunisolar calendar may explain why solar calendars (which have months which no longer relate to the phase of the Moon, but are based only on the motion of the Sun relative to the equinoxes and solstices) have generally replaced lunar calendars for civil use in most societies. Conversely, exclusively lunar calendars such as the Islamic calendar, do not try to synchronise with the solar year. (Consequently, an Islamic year is shorter than a solar year and the Islamic New Year has a different Gregorian calendar date in each (solar) year.)
Months in various calendars.
Beginning of the lunar month.
The Hellenic calendars, the Hebrew Lunisolar calendar and the Islamic Lunar calendar started the month with the first appearance of the thin crescent of the new moon.
However, the motion of the Moon in its orbit is very complicated and its period is not constant. The date and time of this actual observation depends on the exact geographical longitude as well as latitude, atmospheric conditions, the visual acuity of the observers, etc. Therefore, the beginning and lengths of months defined by observation cannot be accurately predicted.
While some like orthodox Islam and the Jewish Karaites still rely on actual moon observations, reliance on astronomical calculations and tabular methods is increasingly common in practice.
Pingelapese, a language from Micronesia, also uses a lunar calendar. There are 12 months associated with their calendar. The moon first appears in March, they name this month "Kahlek". This system has been used for hundreds of years and throughout many generations. This calendar is cyclical and relies on the position and shape of the moon.
Roman calendar.
Roman calendar was reformed several times, the last three enduring reforms during historical times. The last three reformed Roman calendars are called the "Julian", "Augustan", and "Gregorian"; all had the same number of days in their months. Despite other attempts, the names of the months after the Augustan calendar reform have persisted, and the number of days in each month (except February) have remained constant since before the Julian reform. The Gregorian calendar, like the Roman calendars before it, has twelve months, whose Anglicized names are:
The famous mnemonic "Thirty days hath September" is a common way of teaching the lengths of the months in the English-speaking world. The knuckles of the four fingers of one's hand and the spaces between them can be used to remember the lengths of the months. By making a fist, each month will be listed as one proceeds across the hand. All months landing on a knuckle are 31 days long and those landing between them are 30 days long, with variable February being the remembered exception. When the knuckle of the index finger is reached (July), go over to the first knuckle on the other fist, held next to the first (or go back to the first knuckle) and continue with August. This physical mnemonic has been taught to primary school students for many decades, if not centuries.
This cyclical pattern of month lengths matches the musical keyboard alternation of wide white keys (31 days) and narrow black keys (30 days). The note F corresponds to January, and the "diabolis in musica" note F corresponds to February, the exceptional 28–29 day month.
Numerical relations.
The mean month-length in the Gregorian calendar is 30.436875 days.
Any five consecutive months, that do not include February, contain 153 days.
Calends, nones, and ides.
Months in the pre-Julian Roman calendar included:
The Romans divided their months into three parts, which they called the "calends", the "nones", and the "ides". Their system is somewhat intricate. 
The ides occur on the thirteenth day in eight of the months, but in March, May, July, and October, they occur on the fifteenth. The nones always occur 8 days (one Roman ‘week’) before the ides, i.e., on the fifth or the seventh. The calends are always the first day of the month, and before Julius Caesar's reform fell sixteen days (two Roman weeks) after the ides (except the ides of February and the intercalary month).
Relations between dates, weekdays, and months in the Gregorian calendar.
Within a month, the following dates fall on the same day of the week:
Some months have the same date/weekday structure.
In a non-leap year:
In a leap year:
Hebrew calendar.
The Hebrew calendar has 12 or 13 months.
Adar 1 is only added 7 times in 19 years. In ordinary years, Adar 2 is simply called Adar.
Islamic calendar.
There are also twelve months in the Islamic calendar. They are named as follows:
See Islamic calendar for more information on the Islamic calendar.
Hindu calendar.
The Hindu calendar has various systems of naming the months. The months in the lunar calendar are:
These are also the names used in the Indian national calendar for the newly redefined months. Purushottam Maas or Adhik Maas (translit. ' = 'extra', ' = 'month') is an extra month in the Hindu calendar that is inserted to keep the lunar and solar calendars aligned. "Purushottam" is an epithet of Vishnu, to whom the month is dedicated.
The names in the solar calendar are just the names of the zodiac sign in which the sun travels. They are
Baháʼí calendar.
The Baháʼí calendar is the calendar used by the Baháʼí Faith. It is a solar calendar with regular years of 365 days, and leap years of 366 days. Years are composed of 19 months of 19 days each (361 days), plus an extra period of "Intercalary Days" (4 in regular and 5 in leap years). The months are named after the attributes of God. Days of the year begin and end at sundown.
Iranian calendar (Persian calendar).
The Iranian / Persian calendar, currently used in Iran and Afghanistan, also has 12 months. The Persian names are included in the parentheses. It begins on the northern Spring equinox.
Reformed Bengali calendar.
The Bangla calendar, used in Bangladesh, follows solar months and it has six seasons. The months and seasons in the calendar are:
Nanakshahi calendar.
The months in the Nanakshahi calendar are:
Khmer calendar.
Like the Hindu calendar, the Khmer calendar consists of both a lunar calendar and a solar calendar. The solar is used more commonly than the lunar calendar. There are 12 months and the numbers of days follow the Julian and Gregorian calendar.
The Khmer lunar calendar contains 12 months; however, the eighth month is repeated (as a "leap month") every two or three years, making 13 months instead of 12.
Tongan calendar.
The Tongan calendar is based on the cycles of the moon around the earth in one year. The months are:
Sinhalese calendar.
The Sinhalese calendar is the Buddhist calendar in Sri Lanka with Sinhala names. Each full moon Poya day marks the start of a Buddhist lunar month. The first month is Vesak. 
Germanic calendar.
The old Icelandic calendar is not in official use anymore, but some Icelandic holidays and annual feasts are still calculated from it. It has 12 months, broken down into two groups of six often termed "winter months" and "summer months". The calendar is peculiar in that the months always start on the same weekday rather than on the same date. Hence Þorri always starts on a Friday sometime between January 22 and January 28 "", Góa always starts on a Sunday between February 21 and February 27 "".
Old Georgian calendar.
 "New Year in ancient Georgia started from September."
Old English calendar.
Like the Old Norse calendar, the Anglo-Saxons had their own calendar before they were Christianized which reflected native traditions and deities. These months were attested by Bede in his works "On Chronology" and "The Reckoning of Time" written in the 8th century. His Old English month names are probably written as pronounced in Bede’s native Northumbrian dialect. The months were named after the moon; the new moon marking the end of an old month and start of a new month; the full moon occurring in the middle of the month, after which the whole month took its name.
When an intercalary month was needed, a third "Litha" month was inserted in mid-summer.
Old Hungarian calendar.
Nagyszombati kalendárium (in Latin: "Calendarium Tyrnaviense") from 1579.
Historically Hungary used a 12-month calendar that appears to have been zodiacal in nature but eventually came to correspond to the Gregorian months as shown below:
Old Egyptian calendar.
The ancient civil Egyptian calendar had a year that was 365 days long and was divided into 12 months of 30 days each, plus 5 extra days (epagomenes) at the end of the year. The months were divided into 3 "weeks" of ten days each. Because the ancient Egyptian year was almost a quarter of a day shorter than the solar year and stellar events "wandered" through the calendar, it is referred to as Annus Vagus or "Wandering Year".
Nisga'a calendar.
The Nisga'a calendar coincides with the Gregorian calendar with each month referring to the type of harvesting that is done during the month.
French Republican calendar.
This calendar was proposed during the French Revolution, and used by the French government for about twelve years from late 1793. There were twelve months of 30 days each, grouped into three ten-day weeks called "décades". The five or six extra days needed to approximate the tropical year were placed after the months at the end of each year. A period of four years ending on a leap day was to be called a "Franciade". It began at the autumn equinox:
Eastern Ojibwe calendar.
Ojibwe month names are based on the key feature of the month. Consequently, months between various regions have different names based on the key feature of each month in their particular region. In the Eastern Ojibwe, this can be seen in when the sucker makes its run, which allows the Ojibwe to fish for them. Additionally, Rhodes (1993) also informs of not only the variability in the month names, but how in Eastern Ojibwe these names were originally applied to the lunar months the Ojibwe originally used, which was a lunisolar calendar, fixed by the date of "Akiinaaniwan" (typically December 27) that marks when sunrise is the latest in the Northern Hemisphere.