Molecular topological indices are important molecular structural descriptors in the QSRP/QSAR studies of the compounds besides physicochemical and quantum parameters. Molecular topological indices are obtained from molecular ichnographic-topological structure, which is relatively simple. In this work, several new sets of topological indices are proposed as well as some QSPR models. The main results obtained are:1. A method for the calculation of connectivity indices of polymers are developed that can be used to calculate any order connectivity indices of polymers without any truncation errors. Based on this two correlations are proposed for the thermal conductivity of amorphous polymer at room temperature. Because only connectivity indices were used in the proposed correlations, they are general models with good predictive capability.2. Modified connectivity indices as structural descriptors for organic compounds are proposed based on the modified adjacency matrix developed in this work. The results of the QSPR studies on the boiling point temperature, molar volume and molar refraction of alkanes, alkenes and alcohols show that, in most cases, the modified connectivity indices give improved correlations than the original molecular connectivity indices, which are particularly suitable to distinguish isomers.3. Chirality factors that can distinguish enantiomers and diastereomers are proposed which can overcome the disadvantage of the conventional