I was for some time curious about William Feller's probability tract (first volume); luckily, I could lay my hands on it recently and I find it of super qualities. It provides a complete exposition of elementary(no measures) probability. The book is rigorous "hard" math but doesn't escape from giving a solid intuitive feeling. The author discusses a topic, mentions an example, proposes different scenarios that gives back more math. His first chapter on "nature of probability" is essential. It gives a good feeling for what statistical probability means, and why/how it was defined as it is.
Question: I'm looking for other math books on fundamental mathematics(algebra, real analysis, etc...)- essential mathematics that is not very advanced(algebraic geometry for example) - of high qualities like Feller's probability text. Feller might not be used anymore, but its full of exercises that would make it a working textbook written by a master.
To be specific and not too general. I'm looking exactly for inspiring Feller style books in real analysis and abstract algebra. Rudin is good, but its not a master book. I don't know much about abstract algebra available textbooks/master expositions.