There are a lot of reference material about SCRUM available online. To start with you can read the following lists:
SCRUM is a flavor of AGILE. To know the philosophy of AGILE please see the Agile manifesto.
In my opinion SCRUM simply is a way of doing work. People do have a lot of misconceptions when we talk about SCRUM, they think it is a way to solve the problems. But I see it differently, SCRUM will not solve our day-to-day problems, it will just help them to be visible. What we do with our problems is definitely in our hands.
When both of us started on this project, we incidentally were reading a book “The Goal: A Process of Ongoing Improvement ” by Dr. Eliyahu M Goldratt. This book was a point of inflection for both of us, as we were trying to correlate the idea to find bottlenecks in our development process and to some extent how we manage things at our company. Even after 2 years of development we still correlate the incidents of the book and try to solve them.
“The Goal”, explains the “Bottlenecks” (constraints) in manufacturing process, we stuck an analogy of this with our development process we follow. I would recommend this book for anybody who is serious in implementing agile. It is important to note that it is “Critical Thinking and Constant Actions” which can help a system to improve and deliver better results.