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Let's say I already know the rules of the games. What would be the next thing I should focus on? And then? Learning the most common openings? Unbalances?

I learned to play chess as a kid, played once in a while back then but then I have hardly played in 20 years. I've started to play again, and I'd like to improve. I don't want to be extremely good and I don't have a lot of time to invest, I'd just like to achieve a decent level and enjoy playing.

I'd also appreciate a couple of book recommendations, pre-intermediate level.

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Here are some recommendations for your limited time: Solving tactic puzzles is the best way to improve. There are online sources for this but books with the best bang for your buck are: "1001 Winning Chess Sacrifices and Combinations" and "1001 Brilliant ways to Checkmate" both by Fred Reinfeld. Then you need to learn strategic basics so read "My System" by Aron Nimzowitsch. And of course you need basic endgame knowledge so "Basic Chess Endings" by Reuben Fine Memorizing openings isn't going to make you a good player. You can watch videos on youtube for openings but with your time constraints I would not recommend opening books. I do recommend you get a book of games written by the player, some world champion that you like.

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To complete other answers, I'd avise you to play 15 min games or longer time control, avoid blitz at the very beginning. Playing blitz is a very good way to practise opening though, and you speed thinking, but not right now.

Speaking of openings, choose an opening that suits your style (be it a d4 or e4 opening) and stick to it. Play something sound that you intend to play in the long run. For example, a lot of players try to dodge the Sicilian playing McDonnell Attack or Grand-Prix (a bit better than the latter). Those are not totally unplayable but you won't learn a lot and will be crushed against stronger players. You shoud avoid the most theoritical openings, because you'll spend most of you time and efforts remembering moves (or findind them over the board) rather than playing chess.

If you are a d4 player, you'll learn (anyway!) the Queen's gambit declined, to which you can add the Trompovsky (very interesting opening). If you are an e4 player and you're afraid of the open Sicilian, give a try to the Rossolimo.

As black, against e4 and if you're willing to play the Sicilian, I'd recommand the Taimanov. Against d4, it's hard to tell, you have a bunch of choice. The Nimzo is very interesting as well, theoretical of course but maybe not as much as the Grünfeld or King's indian. But once again, it depends on your style.

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Obviously, simply playing the game is the best way to enjoy it and, at the same time, fill your brain with the patterns you need to improve.

If you want to speed up that improvement process without spending a lot of time and while still having fun, the most efficient things are tactics puzzles (there are tons of apps or websites out there) and joining a club (hopefully there's at least one in your town).

Tactics are widely considered to be the most important topic to practice at the beginner to intermediate level in order to get better at the game. Doing puzzles can be done very time-efficiently by using a couple of spare minutes here and a couple of spare minutes there (e.g while waiting for the bus) - you don't have to allocate special "training time"! At the same time, they will pump happiness hormones into your brain by using the psychology of reward stimuli (most apps/sites use some sort of point system to show your progress).

Visiting a club on the other hand will use up some hours per week at a specific time slot - but most clubs try to place their meetings at an employment-friendly time in the evening, so it shouldn't interfere too much with your daily routine. And, of course, meeting with other people is the best way to have fun and enjoy the game! You can also learn a lot by having better players comment on your play. This sort of advice generally is less "complete" than the coverage a book might offer, but it will be specifically tailored to your needs. And it will be a lot less dry, so more of it will actually stick in your memory (properly working with a chess book takes a lot of time - that you might not have - and can quickly develop into a chore).

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Go to your local chess club. They will match you with opponents of an appropriate skill level. In addition, there will be people there willing to help you improve.

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