Can I use contractions in my thesis?
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Many people have different opinions, even among those who are native English speakers and/or think a lot about what makes for good exposition. That said, here are a few rules of thumb:

  1. Your thesis is possibly the most formal writing you will ever do. Survey articles and expository articles (especially for undergrads or other non-experts) are often written less formally. Even many conference proceedings and some journal articles omit some details, and thus can feel less formal than your thesis.

  2. No one will fault you for avoiding contractions altogether. If in doubt, leave it out (the contraction, that is). I hate some techniques common in formal writing, such as overuse of the passive voice, or nearly any use of the pronoun one. But lack of contractions doesn't bother me.

As a more general resource for non-native English speakers, consider Doug West's The Grammar. West has written two textbooks and over two hundred papers, as well as having served as a problem editor for the Math Monthly for the last 20-something years. Surely many people will disagree with at least one piece of advice he gives, but what I find helpful is that West explains his motivation for each piece of advice he offers.