For books I recommend for studying undergraduate mathematics, see my curated list.
For books I recommend for postgraduates and project students in mathematics education or in any area of social science, see below.
Wallace & Wray: Critical Reading and Writing for Postgraduates
This book describes practical strategies for reading efficiently and with writing in mind. I believe that everyone should read it before starting a literature review. For those who are writing up, useful chapters might be those on structuring a dissertation and using the literature in research papers.
Becker: Writing for Social Scientists
This book is great for anyone who finds it difficult to get started on a big piece of work. It is a very easy read – I recently re-read it in a day – and it will cheer you up.
Williams: Style – Ten Lessons in Clarity and Grace (other editions have slightly different titles)
If I could keep only one book, this would be it. Williams explains how to identify bad sentences and how to fix them. He then does the same for paragraphs and larger units of text. In later chapters, he explains ways to make writing not only clear but also elegant.
Strunk & White: The Elements of Style
This is very short and very good. It is less detailed than Williams, but gives clear illustrations showing, for instance, how to write more forcefully.
Evans: How to do Research
Evans writes about the whole process of research, and his chapter on communication has a section about writing that i particularly useful for introductions.
Lunenburg & Irby: Writing a Successful Thesis or Dissertation – Tips and Strategies for Students in the Social and Behavioral Sciences
This book offers prescriptive instructions about what to put in which chapters and sections of a thesis. Different academic areas and expect different things, and its sample texts from actual theses are written by inexperienced writers so they are far from perfect. But the suggestions are useful for structuring troublesome thesis sections like introductions and discussions.
Aldridge & Derrington: The Research Funding Toolkit
This book is an excellent guide to writing proposals for research funding. Like many of the books on this list, it contains detailed, practical, prescriptive advice on what to include where and on how to set about preparing a proposal.
Trask: The Penguin Guide to Punctuation
This is short, concise, and comprehensive. If you have never been quite sure how to use a semicolon, this is the book for you. It is also, improbable though this sounds, funny.
Trask: Mind the Gaffe – The Penguin Guide to Common Errors in English
As in his punctuation book, Trask is entertainingly rude about misuses of numerous words, and about fancy words used needlessly (see ‘utilise’). My copy now falls open at the page that explains common misuses of ‘comprise’, ‘consist’, ‘compose’ and ‘constitute’.