This course offers an introduction to the different physical mechanisms involved in the swimming motion of living organisms ranging from the smallest (bacteria) to larger species (e.g. fish). In both limits, a detailed analysis of the fluid-solid interactions problem, and in particular of the fluid mechanics around the organism, will be presented. Lectures on the fundamentals of the fluid mechanics will be complemented by some on the biological background and description of the relevant characteristics and properties of real organisms, and by short presentations on current research topics in the field.