Positioning techniques and algorithms have been studied for some years at the Tampere University of Technology within several research groups. The objective of this course hand-out has been to collect together the most important algorithms and mathematical tools used in positioning including examples and starting from the basics. We do not go into details of specialized techniques and equipment, but after this course student should be able to solve application dependent problems without having to “re-invent the wheel” again and again. This hand-out and course provide a strong basis for the course TKT-2546 Methods for Positioning. During the previous years courses MAT-45806 Mathematics for Positioning and TKT- 2546 Methods for Positioning had a common hand-out. For practical reasons, the earlier hand-out has been divided into two parts so that both courses now have their own hand-out. Still the courses in question are tightly connected and it is strongly recommended to take both courses the same school year. Prerequisites are first-year engineering mathematics and basics of probability. Additionally, the course TKT-2536 Introduction to Satellite Positioning is a useful but not compulsory prerequi- site. There is no official course text book in addition to this hand-out, mostly because the authors have not managed to find a single book to cover all the material on the level of abstraction we need. The arsenal of positioning computation methods is collected from different areas of mathematics and engineering sciences, and there are often discipline and interpretation differences between them, so we have tried to use common notations and represent connections between different ways of thinking as best as we could. The homepage of the course is http://math.tut.fi/courses/MAT-45806/ which contains additional information about the course and if necessary errata of this hand-out. The authors would like to thank Sami Tiainen for the initial translation of the manuscript, and professor Robert Piché, Helena Leppäkoski, Henri Pesonen, Hanna Sairo, Martti Kirkko-Jaakkola and others who have contributed to the hand-out. The sections excluded from this year’s implementation have been marked with an asterisk (*).