It is very easy, when writing in a second language, to worry about communicating your ideas in accurate language. What very often happens is that students focus on this, but then they forget to connect the ideas. As a result, they write lots of short sentences that don't appear to have any logical connection with each other.
Contrast: It is hot, but I am wearing a winter coat.
Emphasis: I am tired and I am hungry.
Cause and effect: I wanted to eat, so I bought a sandwich.
Of course, these are very simple words; we can use alternative, more formal linkers to connect our ideas in appropriately formal, academic English.
Contrast: Although it is hot, I am wearing a winter coat.
It is hot. Nevertheless, I am wearing a winter coat.
It is hot. However, I am wearing a winter coat.
Despite the fact that it is hot, I am wearing a winter coat.
Despite the heat, I am wearing a winter coat.
Emphasis: I am tired. In addition, I am hungry.
I am tired. What is more, I am hungry.
I am tired. Additionally, I am hungry.
Cause and effect: I wanted to eat. Consequently, I bought a sandwich.
I wanted to eat. Therefore, I bought a sandwich.
I wanted to eat. As a result, I bought a sandwich.
Important! Note how these linkers use a comma after them, and sometimes you have to change the word order.