Best fiction book is a tie between:
The Martian by Andy Weir, for its hard-science attempt. Best description of the book is Andy Ihnatko's (I think, I heard it on a podcast, so I may be wrong): think of it as the 5-minute scene in Apollo 13 when the engineers have to solve the $\mathrm{CO}_{2}$ scrubber problem, except it's an entire book like that. I have quibbles with the science here and there, and its stoichiometry is a bit iffy, but overall -- well, it ties with a Neal Stephenson scifi novel, so that's a major achievement.
Seveneves by Neal Stephenson, for the usual NS reasons: well-researched material, engaging mini-puzzles in the narrative, and interesting story. Plus the second novel that he added at the end, which most writers would have published as a separate book. A number of meta- and meta-meta- references for those of us who like that kind of thing. Despite being 1000-plus pages, I did my usual Stephenson-book thing and read it twice in a row.
Best non-scifi fiction goes to a French book; read the French version, if you can:
Soumission by Michel Houellebec ("Submission" in English), a book that skewers a number of sacred cows of the politically correct, while presenting an… interesting, that's the word, view of Humanities academic life in Europe. Two favorite excerpts, among many:
On peut même, dans une certaine mesure, les persuader de la haute valeur érotique des professeurs d'université (We can, to a certain extent, persuade [marriage brokers] of the high erotic value of university professors - JCS translation).
L'intellectuel en France n'avait pas à être responsable, ce n'était pas dans sa nature (French intellectuals are not expected to be responsible people, that's not in their nature - JCS translation).
Honorable mention in fiction to:
Code of Conduct by Brad Thor, which presents a scary end-of-civilization scenario, unfortunately all-too-possible. Sadly, there are people who actually cheer for that scenario. (I once met someone advocating for a world population of five million. That would be more than a $99.9\%$ reduction, a genocide unparalleled in history.)
Best science book was easier than usual, as I have cut down my reading of science popularization books in favor of reading science textbooks and research papers:
The Science of Interstellar by Kip Thorne is a companion to the movie Interstellar and explains some of the science underlying the story. For those who have the BluRay (like me), the book is a deeper and longer version of the special feature "The Science of Interstellar," with deeper explanations and a few speculative areas. Kip Thorne writes well for a general audience, but he doesn't baby-science the science: despite the accessible prose, thinking is required.
Honorable mention in science to
Dark Matter and the Dinosaurs by Lisa Randall, two concepts that aren't usually put together (as the intro says), is a tour of some new results and some old knowledge in physics written in accessible prose. Like Kip Thorne's book, it requires thinking. (It lost to Thorne because his book had a movie and a documentary attached. :-)
Best nonfiction non-science goes to a combination of two books by the same author:
The 4th-Generation Warfare Handbook and On War by William S. Lind, both illustrate the change in warfare from 3rd-Generation maneuver warfare to 4th-Generation warfare by non-state agents. On War is a book of collected columns and includes quite a few that will jar sensibilities, even considering the topic. The Handbook reads like lecture notes or a textbook for the armed forces or law enforcement, but accessible to the general public. Fair warning: once you learn some of these things, your level of paranoia will increase and your general happiness with the world (hitherto achieved through naïveté) will decrease.
Honorable mention in nonfiction to
The Master Algorithm by Pedro Domingues, a book that will make for many entertaining family dinners for machine learning and artificial intelligence practitioners and researchers. (Because their relatives who read the book will believe that they understand the material to the point where they can debate experts, and that's always entertaining to see.) It covers machine learning at a basic level and makes it easier for non-experts to read articles on automation and decision-support with some understanding of what's going on.
The last book I read in 2015 was a re-read,
Castles of Steel by Robert K Massie, a history of naval combat in World War I. I read it before, of course, when it came out in 2004. Niche appeal to those of us who like to know history (and not from Captain America comic books), have an interest in Europe and Western Civilization, and are nautically-inclined. Despite the topic, little overlap with Dreadnought, by the same author.