You use even to suggest that what comes just after or just before it in the sentence is rather surprising.

You use even with comparative adjectives and adverbs to emphasize a quality that someone or something has.

You use even if or even though to indicate that a particular fact does not make the rest of your statement untrue.

If one thing happens even as something else happens, they both happen at exactly the same time.

You use even so to introduce a surprising fact which relates to what you have just said.

You use even then to say that something is the case in spite of what has just been stated or whatever the circumstances may be.