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Contents

• V Full version
• 0 Introduction
• 1 ϕ⁴ kinks
• 1.1 Kink solutions
• 1.2 Dynamic kink
• 1.3 Soliton interactions
• 1.4 Quantization of kink motion
• 1.5 Sine-Gordon kinks
• 2 Vortices
• 2.1 Topological background
• 2.2 Global U(1) Ginzburg–Landau vortices
• 2.3 Abelian Higgs/Gauged Ginzburg–Landau vortices
• 2.4 Bogomolny/self-dual vortices and Taubes' theorem
• 2.5 Physics of vortices
• 2.6 Jackiw–Pi vortices
• 3 Skyrmions
• 3.1 Skyrme field and its topology
• 3.2 Skyrmion solutions
• 3.3 Other Skyrmion structures
• 3.4 Asymptotic field and forces for B = 1 hedgehogs
• 3.5 Fermionic quantization of the B = 1 hedgehog
• 3.6 Rigid body quantization