The first person wrote a lot of textbooks, which are generally considered to be better. I will supplement Hardy's pure mathematics textbook. Judging from the background you provided, Pure Mathematics will be a good introductory book (photocopied in English, from the Mechanical Engineering Society). Understand this book thoroughly, and you will have a foundation. If the degree is better, add a copy of Apostol's Mathematical Analysis, which I think is more interesting and not so difficult than Rudin's. What needs to be added is that there are still differences between Chinese and foreign writing styles. One of the better textbooks in China can be seen in Concise Calculus written by Professor Gong Sheng of China University of Science and Technology, and Wu Wenjun spoke highly of it.

Regarding Newton's principles, I think many people have misunderstandings now: they think that Newton must be read when reading scientific works, or Newton must be read when reading math books, and so on. In fact, if we study the history of science, principles are very important. However, the content of the principle has been fully developed by later masters. In other words, Newton's research methods have been improved, Newton's symbols have been modernized, and Newton's research results can be used as exercises in analysis or classical mechanics by senior undergraduates.

As for the geometric explanation, Newton had mastered the algebraic form of calculus when he wrote Principles, but he still translated it into geometric form to avoid being severely criticized at that time. Only by mastering the analysis can we understand Newton's system.

Only those who have seen the history of mathematics can understand the details, and what's more, a high school student can't understand them.

The last piece of advice is: since you are interested in developing mathematics, don't say that you are not doing the problem. The problem is the soul of mathematics, and no mathematician can see it from books. Beginners need practice to get familiar with the field of analysis.

Answer: Mathematical analysis is also called analytic analysis ... The basic content is calculus, but some questions have higher viewpoints and some contents are more modern; The curriculum of formal mathematical analysis is different from calculus or advanced mathematics: there will be more pure theories (such as Lesberg integral and real number theory, depending on the intention of the textbook editor) ... The course content in the name of advanced mathematics is calculus plus some analytic geometry ... In short, calculus is the most basic ... Since it is ambitious, you'd better get familiar with these terms as soon as possible ... The contents of calculus textbooks are not much different from each other, but Thomas calculus is more, which does not mean there is any unique depth.