A survey of bounds for the zeros of analytic functions obtained by continued fraction methods -- Rational approximation and interpolation of functions by branched continued fractions -- Polynomial condition of Leja -- Branched continued fractions and convergence acceleration problems -- Two-point Padé-type and Padé Approximants -- Existence of Chebyshev approximations by transformations of powered rationals -- Best Chebyshev rational approximants and poles of functions -- Hyperbolic approximation of meromorphic functions -- Three different approaches to a proof of convergence for Padé approximants -- On the continuity properties of the multivariate Padé—Operator T m,n -- The Marchaud inequality for generalized Moduli of smoothness -- Analytic properties of two-dimensional continued P-fraction expansions with periodical coefficients and their simultaneous Pade-Hermite approximants -- Modification of generalised continued fractions I definition and application to the limit-periodic case -- Convergence acceleration for continued fractions K(an/1), where an ? ? -- Perron-Carathéodory continued fractions -- On approximation of functions by two-dimensional continued fractions -- On the convergence of the multidimensional limit-periodic continued fractions -- Quelques generalisations de la representation de reels par des fractions continues -- Local properties of continued fractions -- A Stieltjes analysis of the K+-p forward elastic amplitude -- Smoothness conditions for Stieltjes measures from Pade approximants -- Exact multisoliton properties of rational approximants to the iterated solution of nonlinear evolution equations -- Application of rational approximations to some functional equations -- Operator rational functions and variational methods for the model operator -- The generalized Schur algorithm for the superfast solution of Toeplitz systems -- Strong unicity in nonlinear approximation.