Textbook in PDF format "This book attempts to show the richness and versatility of one of the most important mathematical tools, such as the Laplace transform. The book is divided into three sections: the 1st devoted to the Laplace transform in mathematics; the 2nd is about the interaction of this mathematical tool with other sciences; and the 3rd presents engineering and technological applications. It is important to note that the research presented here - including a great variety of topics and approaches - illustrate the enormous range of applications of this mathematical tool created more than 200 years ago, which continues being a fundamental research topic - pure and applied - for mathematicians, scientists and engineers"