We have developed a highly efficient method for purification of the recombinant product Aβ(1-40) peptide. The concentration dependence of amyloid formation by recombinant Aβ(1-40) peptide was studied using fluorescence spectroscopy and electron microscopy. We found that the process of amyloid formation is preceded by lag time, which indicates that the process is nucleation-dependent. Further exponential growth of amyloid fibrils is followed by branching scenarios. Based on the experimental data on the concentration dependence, the sizes of the folding nuclei of fibrils were calculated. It turned out that the size of the primary nucleus is one "monomer" and the size of the secondary nucleus is zero. This means that the nucleus for new aggregates can be a surface of the fibrils themselves. Using electron microscopy, we have demonstrated that fibrils of these peptides are formed by the association of rounded ring structures.