The book "Regularity and Irregularity of Superprocesses with (1 + beta)-stable Branching Mechanism" offers a comprehensive analysis of the multifractal properties of densities of stable superprocesses. It presents the latest findings in this research area and provides the reader with a solid understanding of the current state of science. The presentation of the regularity properties of stable superprocesses is self-contained and includes detailed proofs of the main results. This academic book is suitable both as an introductory text for graduate studies and for professionals who wish to engage with the complex aspects of the subject. Through numerous heuristic explanations, technically demanding results and proofs are made accessible, allowing readers to gain a clear intuitive understanding of the underlying concepts and techniques.