Usually, when you want to design launch vehicles, you usually choose the appropriate universities and go to the appropriate departments. If we talk about Moscow, then this is the 601 department of the Moscow Aviation Institute or the departments of SM-1 and SM-2Moscow State Technical University N.E.Bauman. Here I am talking specifically about the design of the launch vehicle and its complex as a whole. In general, the "Aerospace Institute" (former 6th, aerospace faculty) is being trained in Moscow in a wide range of astronautics, and at the Moscow State Technical University. NE Bauman has a special mechanical engineering faculty. Looking at who and how teaches design at specialized departments, it seems to me that soon the design of launch vehicles will become a forgotten secret of ancestors. Fortunately, there is a fairly good literature on this topic. For everyone who wants to master and learn how to design launch vehicles, I give a tip to the books.
If you only want to enter a university or are a junior student, then it is useful to read V.I. Feodosyev. "Fundamentals of rocket flight techniques". The book is written in an accessible language and covers in general all the main points that you need to pay attention to when designing. I believe that for a schoolboy or junior student, this should be the main reference book on rocket science.
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One important addition: when performing theoretical and design work to master the material read, I recommend using a "calculator and pencil". Only by "feeling with pens" you will fully assimilate the material presented in the literature and imbued with the process of designing launch vehicles. Naturally, the calculator can and should be replaced with Excel or MathCad (only without using the built-in integration functions), and the pencil with an electronic drawing board such as AutoCad.