Writing is hard, even for a native speaker. It is much harder for a non-native speaker. The only way to get better at writing is by practising¹. I try to get my students to write early and often. The worse thing that can happen is that you never use some text you wrote. It is better to write first, and then decide what you are going to use.

I find writing a useful way of helping me think. By trying to write down an idea precisely, you often find that you have not thought through your idea properly. This applies to mathematics as well. Often when trying to prove something, there are lots of easy details that you do not bother with. You assume that you fill in the easy details later. You should try to sort out the easy details early to avoid discovering later that the foundations to your proof are made of sand.

Here are various links that over the years I have found interesting and useful.

• Our research group has a collection of links for students on writing. In particular, we have a style guide. Even if you do not follow the style guide, I would recommend that you read it.

• My current favourite style guide is Steven Pinker's book The Sense of Style: The Thinking Person's Guide to Writing in the 21st Century. Steven Pinker is a linguist. Linguists will tell you that grammar should be descriptive and not prescriptive. Even if this is true, then it does not give you a license to write whatever you want and ignore the grammar you learnt at school. If you are writing technical or scientific texts, then your aim should not be to change language, but instead to write clearly so that the reader understands what you are saying. Pinker has some interesting ideas about how to think about writing and grammar. One idea is to think about how your sentence is parsed, and what its parse tree looks like. You should aim to write sentences that are easy to parse. Another idea is that different audiences have different expectations about what is correct. So even if you believe that there is no absolute correct grammar, the rules describe what expectations your audience has.
  Leave the task of changing language to poets and novelists.

• If you want an opinionated but thorough guide to grammar, then try Grammar and Style: For Examination Candidates and Others² by the philosopher Michael Dummett. It will even give you reasons to split infinitives.

• From Stanford here are two interesting links: How to write a paper, and How to give a good talk.

• Common Errors in English by Paul Brians has a list of common confusions.

• Watch Simon Peyton Jones' videos How to write a great research paper, and How to give a great research talk.

• Writing Mathematics has its own special grammar. Every mathematician should read Paul Halmos' How to Write Mathematics. If you google around you will find PDFs. Also read The Grammar According to West, which contains information on many of the conventions that mathematicians assume when they are writing.