This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature. Our exposition is based upon the philosophy that the study of finite...

I. Exterior Algebra.- II. Elementary Differential Systems.- III. Cartan-Kaehler Theory.- IV. Involution and Prolongation.- V. Quasi-Linear Pfaffian Differential Systems.- VI. Higher Order G-structures.- VII. Embeddings of G-structures.