Hyperbolicity of one-relator groups

The goal of this work is to understand whether one-relator group $G=\langle a,b|R(a,b)\rangle$, $R(a,b)$ – relator of a special kind, is hyperbolic or not. There were applied combinatorial and geometric methods by S. Ivanov and P. Schupp, based on the use of the diagrams over a group. The result of this work consists of two theorems which classify group $G$ for all the kinds of $R(a,b)$ except two of them.