I was wondering if anyone knows any good sources for the theory of quadratic forms over fields of characteristic 2 which are written in English?
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This book by Manfred Knebusch starts with the limerick $$\begin{array}{l}\text{A Mathematician Said Who}\cr\text{Can Quote Me a Theorem that’s True?}\cr\text{For the ones that I Know}\cr\text{Are Simply not So,}\cr\text{When the Characteristic is Two!}\end{array}$$ It gives a uniform treatment of quadratic forms in all characteristics including two. 


http://en.wikipedia.org/wiki/Arf_invariant would be a start. 


The Algebraic and Geometric Theory of Quadratic Forms by Elman, Karpenko and Merkurjev is a standard recent reference for the theory of quadratic forms, paying special attention to the differences between the theory of bilinear forms and the theory of quadratic forms in characteristic 2. 

