Hi Michael,

this answer in the form of a letter is my summary with additions to RenéDescartes great little article.

As you were talking about the Giant Chess Puzzle Book this letter is only about tactics.

Up and comer hinted to spaced repetition. As the Romans took from the Greeks: Repetitio est mater studiorum. Repetition is the mother of learning. There are several kinds of repeating and spaced repetition is a very special one.

Under his #4 RenéDescartes wrote about differences between authors about how and what to repeat. This is not only valid for missed problems. A part of this differences should clear away if you add playing strength. 

Playing strength is highly correlated to memory about positions. If you're 1500 you can probably repeat a book of 1000 basic to average problems immediately. If you're 2000 you should work first through another book.

In his blog series about training http://www.qualitychess.co.uk/blog/?cat=12 Aagaard advises learners of doing the training reguarly. Five times 15 minutes a week is better than two hours a week at one day. Make a habit of it.

In (1) I follow RenéDescartes with adding Tisdale, Improve your chess now, as a serious reference about the critics of Kotov.

In (2) about missed problems I have another method with some common features. The missed problems are the ones I'm interested most. I was thinking about adding problems I needed more than 10 minutes to solve them, but left this for the current run. 

First I tried to understand, what I missed. If doing this, you will find different reasons. In my case solving too fast, not seeing a good defence, special kind of double attacks, not seeing mates with queen and bishop were obvious. 

I now have a file of 400 cards of missed problems out of the last three months. Working through this with the goal of classifying more exactly the failures will probably give additional information. Maybe I find sets with this special problems, maybe I have to extract them out of following trainings.

(3) from RenèDescartes is imo a special case of a failure, not seeing opponents answers. Nunn and Dworetzki have delivered fresh material about Emanuel Lasker. Maybe this shows a real master of seeing the opponents possibilities in action. It should, as that's what mamy GM's did say about him.

In reply #5 RenèDescartes rejects to take a set of problems for 30 minutes and adds conditions under which this is useful. For players till my level (Elo just about 2000, national rating 17 points below 2000), if it is about tactics, such sets are useful imo. You must see the idea of some tactics in an otb-game within seconds. So if you take a 30 minutes session over your book you are nearer to the otb situation.

If it is about "more complex" strategical decision I do agree with taking one problem per session. Dworetzki has a training method for this. Think about a position 3 minutes. Write down your results. Think again about this position for 10 minutes and write down. Think again 30 minutes and write down. He forecasts that you will learn better to find critical moments and that you will see your weaknesses not only by failures but also by different results over time spans. But this is not tactical training.

At the end I found Aagaard and his blog about training very useful. The link gets you to the start of this:
http://www.qualitychess.co.uk/blog/?p=1556

Hoping this will help you  ,
Jupp53

Thanks for the appreciative comments!

I wouldn't do a set where all the problems take 30 minutes. There should be a mixture, with some coming right away (within a minute), maybe half of them in under 10 minutes, and others taking a long time, with a few that you can't do at all: pull the plug after 30 minutes. More time than that in a deep think in a game is usually unproductive in my experience.

If you can't see a quick knight fork yet, poring over the problem for 30 minutes is highly inefficient. Learning the basic mechanisms by looking at the answers after 5 minutes is a better strategy at that beginning level. So would be reading a book by Martin Weteschnik where he explains the mechanisms analytically in great detail along with some beautiful examples.

Also, you should know that there are others who disagree strongly with me about long problems. Heisman advocates doing lots of very easy problems repetitively. On the other hand, he touts what he calls a "Stoyko exercise" (even though the Russians and Silman recommended it first), in which you do a long written analysis of a difficult problem, and claims it can add a lot of points to your rating each time you do it (?!). You could do both (I don't). Anyway, experiment attentively and do what works for you!

There is a lot to say about this. 

(1)I do the diagrams iwithout moving the pieces. I scan the board and do a preliminary evaluation of the position. I note the material balance, hanging pieces,  geometrical features such as masked batteries or knight-forkable units, both sides' strengths and weaknesses, etc.. Then I try to note the existence of all the forcing moves, mechanically listing in particular every check and capture. Once I start trying to solve it, if the problem proves difficult I work in writing, spending up to 30 minutes. Writing down the variations does not reduce, rather it even increases, the visualization benefit. Furthermore, it helps me learn how to organize the tree of variations in my mind, a big problem for me, since my short-term memory is not as strong as my analytic intelligence. Here I side with the much-abused Kotov, because while to my mind he goes too far in saying one should analyze each variation once, he is right in saying that it is very important not to think chaotically and to bear the tree of variations in mind. We learn to do algebra in our heads by doing algebra well in writing, and I think the same is true of managing the tree of variations.

(2)Now about the ones I get wrong. This is the most important part, because this is where one  finds out about new mechanisms as well as about what kind of thing one tends to overlook. I circle the problem number in pencil next to the diagram. Then, like Up-and-Comer, I imagine the variations given in the solution in my head.

We can distinguish several cases of missed problems. In the most normal case, the solution is obvious once the main line is pointed out. Here I try to notice what sort of thing I tend to miss repeatedly. For example, I often used to miss a disproportionate number of diagonal queen moves (or queen coverage of escape squares) midway through a mating combination. This is extremely important information, since armed with it I can (a) remind myself to look for such moves in characteristic positions and (b) start a collection of problems in a database with exactly this feature in order to drill myself and destroy the deficiency. If the problem is of a type that I already know I tend to miss chronically, I add it to the preexisting collection.

Another case occurs when the author's solution is not enough to make everything clear. I can't see how to refute a move not given in the solution ("but what if he goes 4.Ne1?"); or else I can't even see why the final position is won. In either case, I set the position up in a database and try to solve it while looking at the unclear position (e.g., after 4.Ne1).  I allow myself to move the pieces. This usually doesn't help; for me the issue is usually a lack not of visualization (not that my visualization is that good) but of either understanding or candidate moves.  Finally if I don't see the point after, say, three minutes of this, I let an engine try to refute my idea. Sometimes the engine does so straight off; sometimes my idea is reasonable. Either way, I grab a pen and append these variations to to the author's written solution.

Still another case occurs when I get the main line but assume that I will have smooth sailing after launching off with the initial idea--and miss a defense entirely, along with its possible refutation. For any variation the author gives in parentheses, I look at only the first move, physically covering the rest. If I didn't see the given defense, I stop reading immediately and treat the situation as a new problem, since in a real game I would be defeated if I couldn't solve that, too. Then I mentally note how that defense works and what made it hard to see. For this reason it is best to get a book that lists lots of variations in the solution. For example, Blokh, Shumilin, Yusupov and Coakley cover a wonderful range of alternative moves in their notes. So does ChessTempo. 

(3) At the end of the problem, I try to train my mind for defense by asking what the other side could do to prevent the combination. Sometimes this is trivial, but other times it is revealing. I am a big believer in prophylactic thinking, and many positive problems can be done negatively this way. Onscreen, I more often than not invert the board and think not "what can I do to him," but "what can he do to me?" . I think this is very beneficial. It can also be helpful to ask what factors might have revealed the likely presence of a combination, correcting or supplementing the reconaissance done at the beginning of the problem.

(4) Regarding what to do later with the missed problems, there is a wide variety of opinions. Some authors (Heisman, Axel Smith) advocate repeating the same problem set (say three hundred problems) until the problems can be done rapidly. Warning: if you do this, repeat them at increasingly wide intervals--do not use the discredited De la Mazza "seven circles" method. Google "spaced-repetition research" and see the blog of EmpiricalRabbit for some information on this. Other trainers, such as Yusupov, say a lot of repetition is probably overkill. I personally am not convinced of the superiority of repeating problems over doing new ones, but I think that maintaining a list of mistakes is important. I sometimes return to books months or years later and go over the circled problems (along with a smattering of others to make sure I can get them easily).

(5) Another point to mention is that it can be good to do concentrated diagram training during the week or two before a tournament or even the afternoon before a game, where it plays the same role as "sharpening" training (speed intervals in the 6-8 weeks before a race) does for runners. Positional and opening study have a reverse-sharpening effect on me in the short term and only improve my performance in the long term. 

Obviously doing all this makes little sense on very easy problems. I am a big believer in doing difficult problems, and I always find that solving hard problems makes me better at the easy ones, whereas the converse is not true.

<Edited to complete the numbering of topics after the passage was quoted>

I think what helped me most was analyzing a puzzle until I saw the full solution in my head. I wouldn't guess until I'd puzzled over it for atleast 15 minutes. If I got it wrong I'd look at the answer and see if I could picture it all working out in my head. I would also reread the puzzle books I had, and see if I could get through the entire book without getting any puzzles wrong. 

That's what worked for me.