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Lattice QCD at finite baryon density suffers from the numerical finite density sign

problem. Strong coupling methods, expanding in the inverse gauge coupling, give rise

to alternative representations of the partition function that can make the sign problem

milder. This Habilitation discusses the strong coupling methods developed by the author

and colleagues to study lattice QCD at vanishing and non-vanishing baryon density. The

main results summarized and covered in the attached papers are (1) chiral symmetry

breaking and its restoration at zero temperature for a large number of flavors, (2) the

QCD phase diagram, in particular the location of the chiral/nuclear critical endpoint,

(3) bulk thermodynamics and (4) Hamiltonian formulation and Quantum Monte Carlo

simulations. Most of the results were obtained via a dual formulation for lattice QCD

derived from a strong coupling expansion. All results are limited to the strong coupling

regime, i.e. valid on coarse lattices, where the sign problem is under control.