In these notes on "Projective Modules and Complete Intersections"
an account on the recent developments in research on this subject
is presented. The author's preference for the technique of Patching
isotopic isomorphisms due to Quillen, formalized by Plumsted, over
the techniques of elementary matrices is evident here. The
treatment of Basic Element theory here incorporates Plumstead's
idea of the "generalized dimension functions." These notes are
highly selfcontained and should be accessible to any graduate
student in commutative algebra or algebraic geometry. They include
fully self-contained presentations of the theorems of
Ferrand-Szpiro, Cowsik-Nori and the techniques of Lindel.
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