I am preparing for exams and understand the proofs of real analysis but when it comes to solving excercises or proving different types of theorems I can't do them.
Also most books I have seen on real analysis don't feature normed spaces so one with this as well as metric spaces would be useful.
Is there a good analysis book to practice questions? preferably free and with hints or answers.
On
The textbook $\mathit{Real\,Analysis \,-\,A \, Long \,Form\,Mathematics \, Textbook}$ by Jay Cummings is used heavily in my department by both undergraduate and graduate students to supplement others texts used by our profs. You could probably find a pdf somewhere, but buying it on amazon is very affordable, less than $20.00 USD. I will post an amazon link below. It should contain what you are looking for.
I really like A Problem Book in Real Analysis by Aksoy and Khamsi. Each chapter contains a brief summary, about 30 questions, and detailed solutions!