Analytic continuation. Borel and Weierstrass continuations. Schwarz reflection principle. Continuation along a path, monodromy theorem. Principle of maximum (minimum) modulus. Meromorphic functions. The number of zeros and poles of a meromorphic function within a bounded region is finite. Integral along a simple closed curve of a meromorphic function multiplied by an analytic one: generalized principle of the argument. Index of a closed curve. Principle of the argument. Formula of the inverse function. Abel-Plana formula. Rouché theorem. Determination of the number of zeros of an analytic function within a given region. Harmonic and conjugate harmonic functions. The function \(f=u+\mathrm{i} v\) is analytic if and only if v is harmonic conjugate to u. Existence of the conjugate harmonic function and its determination. Laplace’s and saddle point methods.