There are two main kinds of conjunctions:

Coordinating conjunctions
Subordinating conjunctions

Coordinating conjunctions join two clauses or sentences of equal rank. Here both clauses are capable of being principal clauses if they appear as such in separate sentences.

A subordinating conjunction joins a principal or main clause and a subordinate clause. Note that a subordinate clause cannot stand on its own and doesn’t make complete sense.

Coordinating conjunctions

The most common coordinating conjunctions are: and, but, or, nor, either…or, neither…nor, yet, not only… but also…, both…and.

Coordinating conjunctions are of four kinds:

Additive (cumulative or copulative) conjunctions

An additive conjunction merely adds one statement to another. It doesn’t express ideas such as contrast, choice or inference. Examples are: and, also, too, as well as, both…and, not only…but also…

He walked into the room and sat on the sofa. (Here the additive conjunction and merely adds the clauses ‘he walked into the room’ and ‘he sat on the sofa’.)
He was not only abused but also beaten. (Here the additive conjunction not only…but also… joins the two clauses ‘he was abused’ and ‘he was beaten’.)
These lessons are both free and useful.

Adversative coordinating conjunctions

They express a contrast between two statements in a sentence. Examples are: but, nevertheless, however, whereas, only, still etc.

He is poor but he is honest.
Wise men love truth, whereas fools shun it.
The captain was annoyed, still he kept quiet.
She was late, still she was not punished.

Alternative conjunctions

Alternative conjunctions express a choice between two alternatives. Examples are: or, nor, either…or, neither…nor, otherwise, else etc.

He is either a fool or a rogue.
You must leave this place at once or you will have to face the consequences.
Neither a borrower, nor a lender be.
He knows nothing about this work, neither does he try to learn anything about it.

Inferential or illative conjunctions

These conjunctions introduce some inference. Examples are: therefore, for, so etc.

Work hard, for nobody can succeed without hard work.
He was lazy, therefore, he failed.