Capablanca says

A passed pawn increase in strength as the number of pieces on the board diminishes.

A good player is always lucky.

You may learn much more from a game you lose than from a game you win. You will have to lose hundreds of games before becoming a good player.

In order to improve your game, you must study the endgame before everything else. For whereas the endings can be studied and mastered by themselves, the middle game and end game must be studied in relation to the end game.

I have not given any drawn or lost games, because I thought them inadequate to the purpose of the book (in 'My Chess Career', published in 1920).

Endings of one rook and pawns are about the most common sort of endings arising on the chess board. Yet though they do occur so often, few have mastered them thoroughly. They are often of a very difficult nature, and sometimes while apparently very simple they are in reality extremely intricate.

The best way to learn endings, as well as openings, is from the games of the masters.

The winning of a pawn among good players of even strength often means the winning of the game.

The king, which during the opening and middlegame stage is often a burden because it has to be defended, becomes in the endgame a very important and aggressive piece, and the beginner should realize this, and utilize his king as much as possible.

An exception was made with respect to me, because of my victory over Marshall. Some of the masters objected to my entry, one of them was Dr. Bernstein. I had the good fortune to play him in the first round, and beat him in such fashion as to obtain the Rothschild prize for the most brilliant game, a profound feeling of respect for my ability remained throughout the rest of the contest.

Morphy gained most of his wins by playing directly and simply, and it is simple and logical method that constitutes the true brilliance of his play, if it is considered from the viewpoint of the great masters.

He was a pioneer and one of the most profound researchers into the truth of the game, which was hidden from his contemporaries --- on Wilhelm Steinitz.

None of the great players has been so incomprehensible to the majority of amateurs and even masters, as Emanuel Lasker.

When you sit down to play a game you should think only about the position, but not about the opponent. Whether chess is regarded as a science, or an art, or a sport, all the same psychology bears no relation to it and only stands in the way of real chess.

To improve at chess you should in the first instance STUDY THE ENDGAME.

Alekhine evidently possesses the most remarkable chess memory that has ever existed. It is said that he remembers by heart all the games played by the leading masters during the last 15-20 years.

Most players do not like losing, and consider defeat as something shameful. This is a wrong attitude. Those who wish to perfect themselves must regard their losses as lessons and learn from them what sorts of things to avoid in the future.

The weaker the player the more terrible the Knight is to him, but as a player increases in strength the value of the Bishop becomes more evident to him, and of course there is, or should be, a corresponding decease in his estimation of the value of the Knight as compared to the bishop.

Chess can never reach its height by following in the path of science. Let us, therefore, make a new effort and with the help of our imagination turn the struggle of technique into a battle of ideas.

The game might be divided into three parts, the opening, the middle-game and the end-game. There is one thing you must strive for, to be equally efficient in the three parts.

An hour's history of two minds is well told in a game of chess.

Your Soviet players are cheating, losing the games on purpose to my rival, Botvinnik, in order to increase his points on the score. (to Stalin in Moscow 1936, where he finished clear 1st, one point ahead of Botvinnik)

Chess is something more than a game. It is an intellectual diversion which has certain artistic qualities and many scientific elements.

During the course of many years I have observed that a great number of doctors, lawyers, and important businessmen make a habit of visiting a chess club during the late afternoon or evening to relax and find relief from the preoccupations of their work.

Sultan Khan had become champion of India at Indian chess and he learned the rules of our form of chess at a later date. The fact that even under such conditions he succeeded in becoming champion reveals a genius for chess which is nothing short of extraordinary.

Ninety percent of the book variations have no great value, because either they contain mistakes or they are based on fallacious assumptions; just forget about the openings and spend all that time on the endings.

Although the Knight is generally considered to be on a par with the Bishop in strength, the latter piece is somehat stronger in the majority of cases in which they are opposed to each other.

The great World Champions Morphy, Steinitz, and Lasker were past masters in the art of Pawn play; they had no superiors in their handling of endgames. The present World Champion has not the strength of the other three as an endgame player, and is therefore inferior to them.

To my way of thinking, Troitzky has no peer among endgame compsers; no one else has composed so many and such varied endings of the first rank.

No other great master has been so misunderstood by the vast majority of chess amateurs and even by many masters, as has Emanuel Lasker.

That he was a great endgame player is unquestionable. In fact, he was the greatest I have ever known. But he was also the most profound and the most imaginative player I have ever known.  -  (on Emanuel Lasker)

People who want to improve should take their defeats as lessons, and endeavor to learn what to avoid in the future. You must also have the courage of your convictions. If you think your move is good, make it.