This book contains the refereed papers which were presented at the interna- tional conference on Multivariate Approximation and Splines held in Mannheim Germany on September 7-10 1996. Fifty experts from Bulgaria England France Israel Netherlands Norway Poland Switzerland Ukraine USA and Germany participated in the symposium. It was the aim of the conference to give an overview of recent developments in multivariate approximation with special emphasis on spline methods. The field is characterized by rapidly developing branches such as approximation data fit- ting interpolation splines radial basis functions neural networks computer aided design methods subdivision algorithms and wavelets. The research has applications in areas like industrial production visualization pattern recognition image and signal processing cognitive systems and modeling in geology physics biology and medicine. In the following we briefly describe the contents of the papers. Exact inequalities of Kolmogorov type which estimate the derivatives of mul- the paper of BABENKO KOFANovand tivariate periodic functions are derived in PICHUGOV. These inequalities are applied to the approximation of classes of mul- tivariate periodic functions and to the approximation by quasi-polynomials. BAINOV DISHLIEV and HRISTOVA investigate initial value problems for non- linear impulse differential-difference equations which have many applications in simulating real processes. By applying iterative techniques sequences of lower and upper solutions are constructed which converge to a solution of the initial value problem.