This book by M. do Carmo, winner of the 1992 Mathematics Price of the Third World Academy of Sciences, gives an introduction to the theory of differentiable forms. Since it only assumes elementary calculus and elementary linear algebra, it is suitable for second year undergraduate and graduate students in mathematics and physics.
well-established, easy-going introduction
Manfredo P. Do Carmo
Diferential forms Differentialformen begleitendes Dreibein differential geometry differential geometry of surfaces differential manifolds differenzierbare Mannigfaltigkeit eingebettete Flächen immersed surfaces intrinsic geeometry of surfaces intrinsische Geometrie von Flächen manifold moving frames
M.P. Do Carmo
Differential Forms and Applications
"This book treats differential forms and uses them to study some local and global aspects of differential geometry of surfaces. Each chapter is followed by interesting exercises. Thus, this is an ideal book for a one-semester course."—ACTA SCIENTIARUM MATHEMATICARUM