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Could you recommend any approachable books/papers/texts about matroids (maybe a chapter from somewhere)? The ideal reference would contain multiple examples, present some intuitions and keep formalism to a necessary minimum.

I would appreciate any hints or appropriate sources.

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Dover has released a cheap version of Welsh's Matroid Theory - can't argue with the price. On the other hand, I've heard better things about Oxley's Matroid Theory.

(Apparently there is absolutely no creativity in naming books on Matroid Theory)

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You could have a look at the relatively new book

Gary Gordon, Jennifer McNulty: Matroids. A Geometric Introduction, Cambridge University Press 2012.

From the description: "This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students."

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There is a great introduction to matroids that is about 40 pages, free, and sounds more like what you are looking for: What is a matroid? by James Oxley, available from the author's webpage.

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