differential calculus in the complex plane c
��.1 complex numbers
��.2 convergent sequences and series
��.3 continuity
��.4 complex derivatives
��.5 the cauchy-riemann differential equations

�� integral calculus in the complex plane c
��.1 complex line integrals
��.2 the cauchy integral theorem
��.3 the cauchy integral formulas

����sequences and series of analytic functions, the residue��theorem
��.1 uniform approximation
��.2 power series
��.3 mapping properties of analytic functions
��.4 singularities of analytic functions
��.5 laurent decomposition��a appendix to iii.4 and iii.5
��.6 the residue theorem
��.7 applications of the r,esidue theorem

�� construction of analytic functions
��.1 the gamma function
��.2 the weiers'rrass product formula
��.3 the mitrrac_leffler partial fyaction decomposition
��.4 the riemann mapping theorem
a appendix : the homotopical version of the cauchy��integral theorem
b appendix : a homological version of the cauchy
integral theorem
c appendix : characterizations of elementary domains

�� elliptic functions
��.1 liouville's theorems
a appendix to the definition of the period lattice
��.2 the weierstrass -function
��.3 the field of elliptic functions
a appendix to sect. v.3 : the torus as an algebraic curve
��.4 the addition theorem
��.5 elliptic integrals
��.6 abel's theorem
��.7 the elliptic modular group
��.8 the modular function j

�� elliptic modular forms
��.1 the modular group and its fundamental region
��.2 the k/12-formula and the injectivity��of the j-function
��.3 the algebra of modular forms
��.4 modular forms and theta series
��.5 modular forms for congruence groups
a appendix to v1.5 : the theta group
��.6 a ring of theta fhnctions

����analytic number theory
��.1 sums of four and eight squares
��.2 dirichlerr series
��.3 dirichlet series with functional equations
��.4 the riemann <-function and prime numbers
��.5 the analytic continuation of the <-function
��.6 a tauberian theorem

�� solutions to the exercises
��.1 solutions to the exercises of chapter ��
��.2 solutions to the exercises of chapter ��
��.3 solutions to the exercises of chapter ��
��.4 solutions to the exercises of chapter ��
��.5 solutions to the exercises of chapter ��
��.6 solutions to the exercises of chapter ��
��.7 solutions to the exercises of chapter ��
r/eferences
symbolic notations