Basics of a photon collider

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This small review is devoted to $γγ$ collisions including methods of creating the colliding $γγ$ beams of high energy and physical problems which can be solved or clarified in such collisions. Contents: 1. Introduction 1.1. The subject 1.2. Interaction of photons in the Maxwell theory and QED 2. Collisions of equivalent photons at $e^+e^-$ storage rings 3. Results obtained in virtual $γ^*γ^*$ collisions 4. Linear $e^{\pm} e^-$ collider 5. Photon collider on a base of a linear $e^{\pm} e^-$ collider 5.1. Idea of high-energy $γγ$ and $γe$ colliders with real photons 5.2. Scheme of a photon collider 5.3. Compton scattering as a basic process for $e\to γ$ conversion 6. Physics of $γγ$ interactions 7. Concluding remarks 7.1. Summary from TESLA TDR 7.2. Prediction of Andrew Sessler in 1998 7.3. Conclusion of Karl von Weizsäcker for young physicists
22 pages, 19 figures, Lectures given for young physicists in the series of dedicated lectures on Physics at Future Colliders (LHC, ILC, PLC) and Astrophysics at the International Conference ``The PHOTON: its first hundred years and the future'' (30.08 -- 08.09.2005, Warsaw and Kazimierz, Poland)

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