This text is partly based on courses that I taught at the Instituto de Matematica Pura e Aplicada, Rio de Janeiro in 1958 and 1967, at the Universidade do Recife in 1959, and at the Universidade de Sao Paulo in 1967. It reproduces literally a course that I taught at the University of Rochester during the Fall of 1967.
These lectures were intended as an elementary introduction to several complex variables, arranged to lead to certain features of the subject having no counterpart in a standard treatment of one complex variable. Local properties seem to be especially suitable in giving a beginner in the field a flavor of how several complex variablesdiffer from one complex variable. Limitation in time and the desire to present the material in an explicit form had their natural implication in the style of the course. The readers of this volume are encouraged to use the materia quoted in the Bibliography in order to further their study in the direction of local and global complex analysis as needed in present-day mathematics and physics.

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