Journal of Approximation Theory and Applied Mathematics (ISSN 2196-1581) is a journal which started in 2013. Themes of our journal are: Approximation theory (with a focus on wavelets) and applications in mathematics like numerical analysis, statistics or financial mathematics. Contents 2013 Vol. 1: An Approximation on a Compact Interval Calculated with a Wavelet Collocation Method can Lead to Much Better Results than other Methods, Parameter Identification with a Wavelet Collocation Method in a Partial Differential Equation, An Approach for a Parameter Estimation with a Wavelet Collocation Method, Notes on Nonparametric Regression with Wavelets, Extrapolation and Approximation with a Wavelet Collocation Method for ODEs 2013 Vol. 2: Solving ODEs and DAEs with a Wavelet Collocation Method with Examples from the Chemical Reaction Kinetics, Solving Integral Equations with a Wavelet Collocation Approach, Approximation of Non L2(R) Functions on a Compact Interval with a Wavelet Base, Comparing Approximations of a Wavelet Collocation Method of Various Wavelets