This book provides an insight into the process of reformation [or reformation process] [that] the Soviet theatre was undergoing in the early 1930s.
The sentence is fine as it is, but I would add a "that" between "reformation" and "the" for flow and clarity. When the clauses are a bit longer, a "that" helps clarify that it is a clause.
Question: When you say "theatre," are you referring to drama on stage? Or are you referring to other "theaters," e.g., politics? I'm sure if I had more context I wouldn't have to ask.