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The top quark was discovered in 1995 [1, 2] and it is still the heaviest elementary particle known today. Thanks to its large mass, and the related strength of its coupling to the Higgs boson, the top quark may be a key player in understanding the details of electroweak symmetry breaking. Studies of the top quark properties at the Tevatron and Run I of the LHC have given us a detailed understanding of many properties of this particle, including its mass, production and decay mechanisms, electric charge and more. With the exception of the large forward-backward asymmetry in tt¯ production that has been observed at the Tevatron, all results on top quark pairs and single top production obtained so far have been consistent with the Standard Model. We note that in this context, the anomaly in the b quark forward-backward asymmetry observed at LEP might get amplified for the much heavier top quark. In the short and mid-term future, top quark studies will be mainly driven by the LHC experiments. Exploration of top quarks will, however, be an integral part of particle physics studies at any future facility. Future lepton colliders will have a rich top quark physics program which would add to our understanding of this interesting quark. Detailed simulation studies have been carried out for linear electron-positron machines (ILC and CLIC). First attempts have been made to extrapolate these to the case of a circular machine (TLEP). In this report we describe what can be achieved based on projection studies for the LHC and for future lepton colliders. The report is organized along six topics: • Measurement of the top quark mass; • Studies of kinematic distributions of top-like final states; • Measurements of top quark couplings; • Searches for rare decays of top quarks; • Probing physics beyond the Standard Model with top quarks; • Algorithms and detectors for top quark identification at future facilities. Main conclusions for each topic are presented in Sect.1.8.

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