Book Recommendation: Introduction to probability theory (including stochastic processes) I'm a first year undergraduate engineering student and we've got a course "Introduction to Probability Theory" which roughly covers the following topics:

addition, multiplication, marginal and conditional probability, joint
  probability, Baye’s theorem, random variables, probability mass
  function, probability distribution function, moments and moments
  generation function, binomial distribution, Poisson distribution,
  exponential distribution, Gaussian /normal distribution, gamma
  distribution, Chebyshev’s inequality, Schwartz inequality, q function,
  random process, autocorrelation, auto covariance function, stationary
  process, Erlang process, ergodic random process, Markov chain and
  transitional probability, order of Markov chain, Chapman-Kolmogorov
  equation, irreducible state, absorbing state, ergodoic chain, birth
  and death process, Markovian queuing models

It would be very helpful if someone could suggest me a good book which covers all the above topics, because I searched on the net but no book seems to cover all the topics. Also our professor didn't suggest any book as such, but it would be helpful to have one because sometimes the professor's explanations can be confusing.

As a mathematics student I've had courses on probability theory and stochastic processes, and for both of those courses used the book Probability Theory and Random Processes by Grimmet and Stirzaker. The explanations were clear, and I remember the exercises in the book to be quite challenging. At least in my experience back then, but I didn't have any previous experience with probability theory at that point.
Just had a look through the Contents, and it seems to cover pretty much all your topics (as far as I can tell from the contents).
Hope that helps.
