Links and references
I am listing a few good books and articles that talk about systems theory and systems thinking. I have not tried to list all the ones I have ever seen, just the one that I think are useful to beginning systems thinkers. I have also tried to list items that do not overlap too much in their contents.
An Introduction to General Systems Thinking, Gerald M. Weinberg
This book has been widely read and highly recommended by many readers over the years. It focuses on the question of how we gather data and define systems in order to solve problems. Of all the books, this is probably the best place to start.
Systems Thinking, Second Edition: Managing Chaos and Complexity, Jamshid Gharajedaghi
Many readers rate this as the best on the application of systems thinking to organizational and management. It has little mathematical content and emphasizes on social relations and communication.
Thinking in Systems: A Primer, Donella H. Meadow
Meadow gives a very clear introduction to systems model building using the "source, sink, flow" diagramming approach. If you plan to draw systems diagrams, this is a good place to start. (You will also want diagramming software such as OmniGraffle.)
The Image: Knowledge in Life and Society, Kenneth E. Boulding
Boulding was one of the great "systems thinkers" and this analysis of how we construct mental models of the world is among his best.
General system theory: Foundations, Development, Applications, Ludwig von Bertalanffy
Early in the 20th century, biologist von Bertalanffy coined the term "general systems theory." His book on the subject of living systems is still readable and interesting.
General Principles of System Design, Weinberg, Gerald M. and Daniela
This follow on to An Introduction to General Systems Thinking picks up where the first book left off to give a more detailed description of the modelling process.
An introduction to cybernetics, William Ross Ashby (Note: the book is often out of print, but this link takes you to an online version on the web.)
This is a very technical book ... not mathematics, but logic ... that introduces the nitty-gritty of turning data into digital models.
Social systems, Niklas Luhmann
This is a difficult but extremely rewarding development of systems theory as philosophy. It may be on its way to being one of the more influential books of our times.
The Art of Problem Solving: Accompanied by Ackoff's Fables, Russell L. Ackoff
Ackoff provides a collection of interesting problems, the solutions to which illustrate the methods of the systems approach.
Are Your Lights On?: How to Figure Out What the Problem Really Is, Donald C. Gause; Gerald M. Weinberg
Although this is actually a book on how to become a good consultant, Weinberg is a strong advocate of systems, and his examples illustrate a wide variety of problems and solutions.
The Systems Bible: The Beginner's Guide to Systems Large and Small, John Gall
A tongue-in-cheek discourse, this interesting book focuses on the problems that systems themselves present when they fail ... or fail to perform as expected.