I noticed you didn't include the huge Polgar book "Chess" which is nothing but problems. I can't speak for the quality as I haven't worked many of them yet.
Best Composition Collections? Endgame Studies and Problems

Thanks @mldavis617, I had a copy of Polgar's book when I was starting out, but at the time I wasn't interested in the composed mates in 2 and 3. I am intending to get another copy now.

I got a hold of two other collections recently. One is W. Baird's 700 Chess Problems available in the public domain as a pdf. It is a collection of composed mates. The other is Troitzky's Chess Handbook of 360 Brilliant and Instructive Endgames. Thus far it is excellent.

http://www.chess.com/download/view/problemist-22
Problemiste is problem solving software. Not waht you're looking for, I know, but you ban download Anthologies (pbm ext) which you can open in the program.
There are literally tens of thousands mate in X moves problems availsble. Also Helpmates, selfmates, reflexmates etc
There are some limitations if you dont register (cant remember how much money they want) but the free version is functional to such an extent that I dont think its necessary

@rooperi, this is fantastic! Thank you so much. For future searchers, the website is problemist.com, and they have a link on their homepage to over 100,000 downloadable problems (http://www.sudoktor.com/prb/collecto.html).
I think I still like my problems in book form so they are portable (It says there is a pocket PC version, so maybe there be android or iOS versions in future...), and I enjoy a little history about the composer and problem, but this is undeniably great.

Glad you like it, I'm a big fan.
Of course it's also great to check your own compositions for multiple solutions etc.
Most problems come with some info, Composer, date, where it was first published etc. I used to have a 'thing' about people posting unattributed problems, and used the directory search function to find the info.
Nowadays I dont care so much :)

@Mandy711, interesting, I just saw this database discussed in an article on chesscafe. It looks amazing.

There should be a database of all published chess problems. It's not easy to compose a problem. What a waste if the composition was already composed in some chess problem book.
Out of the 5 books listed by SamCopeland:
(Nunn's Solving in Style, Hesse's The Joys of Chess: Heroes, Battles and Brilliancies,Velimirovic's and Valtonen's Encyclopedia of Chess Problems, Kasparyan's Domination in 2545 Endgame Studies,Dvoretsky's Studies for Practical Players)
as a collection of composed endame studies I would rate Kasparyan's Domination in 2545 studies as the alltime best book of Studies, and The Encyclopaedea of Chess Problems as the best for problems. Hesse's book is rather a cornucopia and entertaining, and 'Solving in Style' is dedicated to a specific purpose.
I have a copy of the Domination 2545 for the last 30 years and a dip into it anytime is tremendously enjoyable. It is a book that never dates and the best Study book ever published. I have a large number of books dedicated to studies, including Lommer's 2 volumes, Roycrofts books, Trotstky's complete studies,and many other classics in my library, but this is my considered opinion.


Sam i am going to buy Kasparyan's Domination in 2545 Endgame Studies can u tell me please is it hard and will it teach me anything ? thnaks

@Volencho99, it is hard. It will teach you a ton if you can work through it. I've only done a small portion, but admittedly even a small portion is a lot of problems.

Two books that should be in everyone's library.
1. Basic Chess Endings by Reuben Fine. This book starts with basic king and pawn endings and goes through goes through all rook and pawn, two bishop, and all other combinations. Reuben Fine is a natural born teacher and he explaines what is going on in a position. The explanation is in English not just variation lines. When I started to seriously play it was considered the bible of the endgame.
2. The Ideas Behind The Chess Openings by Reuben Fine is a tremendous book on the openings. Again it explaines the basic ideas behind the moves of openings.
He also wrote: The Middle game in chess.
Can someone please explain to me how to run Problemist? When I open the anthology file 2 from sudoktor.com it just shows the position and immediately lists the different solutions. Is this the way it's supposed to be? I presumed that it would show me the position and let me play to see if I can guess the mates, yes?
Also take a look at www.arves.org which is an endgamestudy association which has much information and examples to replay and a lot of free documentation.

Not a book of compositions per se, but, a book about composing is Chess Wizardry by John Rice.
It seems there is much more to composing than just placing pieces on the board in a tricky way. It is a specialized area, with its own vocabulary, concepts, and heros. This book might tell you more than you ever want to know about composing. Interesting!
http://www.amazon.com/Chess-Wizardry-Problems-Batsford-chess/dp/0713480130/ref=sr_1_1?ie=UTF8&qid=1449529806&sr=8-1&keywords=chess+wizardry
I have recently developed an interest in chess compositions - both composed endgame studies and composed problems. I have a few books that I like so far, but I would really appreciate more suggestions. It seems to be a slightly obscure chess book category so I am finding it harder than usual to find out what is available, and what is quality.
The books I currently have are...
Excepting Kasaryan's book which is basically raw positions and moves, I recommend these all - especially Joys of Chess!
Thanks in advance for any suggestions