This chapter introduces the concept of quarks and gluons as fundamental constituents of hadronic particles, supported by experimental evidence from deep inelastic scattering, low-energy hadronic spectroscopy, and the behavior of low-lying hadrons. The chapter discusses the challenges in producing isolated quarks in experiments and the theoretical framework of non-Abelian gauge theories to explain confinement. It highlights the importance of lattice regularization in studying these theories due to the non-perturbative nature of strong interactions. The chapter also covers the basics of lattice field theory, including the transfer matrix formalism and the connection between statistical mechanics and quantum mechanics through path integrals. It provides a detailed derivation of the propagator for a free scalar field on a lattice and introduces the concept of anticommuting variables for fermionic fields, necessary for lattice formulations of fermionic theories.This chapter introduces the concept of quarks and gluons as fundamental constituents of hadronic particles, supported by experimental evidence from deep inelastic scattering, low-energy hadronic spectroscopy, and the behavior of low-lying hadrons. The chapter discusses the challenges in producing isolated quarks in experiments and the theoretical framework of non-Abelian gauge theories to explain confinement. It highlights the importance of lattice regularization in studying these theories due to the non-perturbative nature of strong interactions. The chapter also covers the basics of lattice field theory, including the transfer matrix formalism and the connection between statistical mechanics and quantum mechanics through path integrals. It provides a detailed derivation of the propagator for a free scalar field on a lattice and introduces the concept of anticommuting variables for fermionic fields, necessary for lattice formulations of fermionic theories.