**Volume 1**

Chapter 1:
*Holomorphic and real analytic calculus*

Chapter 2:
*The Weierstrass Preparation Theorem and applications*

Chapter 3:
*Domains of holomorphy and notions of convexity in*
**C**^{n}

Chapter 4:
*Holomorphic and real analytic manifolds*

Chapter 5:
*Metric structures and connections*

Chapter 6:
*Holomorphic and real analytic jet bundles*

Chapter 7:
*Stein and real analytic manifolds*

Chapter 8:
*Topologies for spaces of maps, functions, sections, and germs*

Appendix A:
*General versions of the Chain Rule and the Leibniz Rule*

Appendix B:
*Convex analysis*

Appendix C:
*Topology background*

Appendix D:
*Distributions*

Appendix E:
*Operator theory*

Appendix F:
*Multilinear algebra*

**Volume 2** (what little there is, at present)

Chapter 1:
*Sheaf theory*

Chapter 2:
*Category theory*

Chapter 3:
*Homological algebra*

Chapter 4:
*Sheaf cohomology*

Chapter 5:
*Coherent sheaves*

Chapter 6:
*Differentiable and analytic spaces*

Chapter 7:
*Approximation*

**Sources:**

*Several complex variables and holomorphic differential geometry:*

- Jean-Pierre Demailly,
*Complex Analytic and Differential Geometry*, pdf - Lars Hörmander,
*An Introduction to Complex Analysis in Several Variables*, Second Edition, North-Holland, Amsterdam/New York, 1973, ISBN 0-444-10523-9 - R. Michael Range,
*Holomorphic Functions and Integral Representations in Several Complex Variables*, number 108 in Graduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg-Berlin, 1986, ISBN 0-387-96259-X - Joseph L. Taylor,
*Several Complex Variables with Connections to Algebraic Geometry and Lie Groups*, number 46 in Graduate Studies in Mathematics, American Mathematical Society, Providence, Rhode Island, 2002, ISBN 0-8218-3178-X

- Hans Grauert,
*On Levi's problem and the imbedding of real-analytic manifolds*, Annals of Mathematics. Second Series,**68**, 450-472, 1958 - Stephen G. Krantz and Harold R. Parks,
*A Primer of Real Analytic Functions*, Second Edition, Birkhäuser Advanced Texts, Birkhäuser, Boston/Basel/Stuttgart, 2002, ISBN 0-8176-4264-1

- Henri Cartan,
*Variétés analytiques réelles et variétés analytiques complexes*, Bulletin de la Société Mathématique de France,**85**, 77-99, 1957 - Hans Grauert and Reinhold Remmert,
*Coherent Analytic Sheaves*, number 265 in Grundlehren der mathematischen Wissenschaften, Springer-Verlag, New York-Heidelberg-Berlin, 1984, ISBN 3-540-13178-7 - Taylor above