This is a seven-year post but I am putting here my experience learning mathematics as an undergraduate.
First, I would explain a bit what's usually inside a mathematics book. For every chapter or sections, there are usually two parts, the contents and the exercises. The purpose of contents is to let you expose yourself to the knowledge while the exercises are to let you improve until you really understand the material well. So, first and foremost, do not feel disappointed if you cannot solve some of the exercises as you have met the exercise at your level! If you can solve all exercises easily or it's so hard that you can't solve any of them, that book is not for you. For me, a book suitable for you would be the one you can solve at least 60% of the questions most of the time. Also, do not try to solve every single exercise in a book as it leads to diminishing returns. There are a lot of fun subjects that you should go for it. This paragraph is to let you have a correct attitude towards exercises in mathematics. Now I will share my way to study a mathematics book.
The first level - Read the chapters briefly. If you are following a course, lecture's class would be at this level. If you are self-studying, read a chapter that you can understand at least half of the content including proofs. If at this point, it takes so long for you to understand (even the first chapter), consider changing to an easier book.
The second level - Read the chapters in detail. Jot down the concept or part of proofs that you can't understand. Copy down all the theorem statements and definitions on a piece of paper. This is extremely helpful when you attempt the exercises.
The third level - Do the exercises in each chapter. After struggling, do not feel embarrassed to look the answer to the questions you cannot solve. Make sure to understand how they solve it.
The fourth level - After you have completed half of the book. It's time for revision! Try to prove everything in the text once again. Revise the exercise that you had done. If you can't prove some of them, reread again and try to memorise the key parts of the proofs. Then reprove them after a few days.
The fifth level - First you do the same as in the fourth level to the last half of the book. Then, write a revision sheet for all the chapters. This revision sheet is for your future reference, so it should be short and concise.
Usually, you can read 4 mathematics book in 3 months by following this process provided the level of the book is suitable for you. After this, you may study another subject of your interest or further sharpen your skills by reading a more advanced text of the same subject. For me, it's the fastest way. Of course, to do this, you need to invest at least 8 hours per day on it.