In modern physics, symmetries are a powerful tool to constrain the form of equations, namely the Lagrangian that describes the system. Equations are assumed to be invariant under the transformation of a given group, which may be discrete or a continuous Lie group. Classification of the various types of symmetry. The concept of spontaneous symmetry breaking. It will evolve into the Higgs mechanism, which gives origin to the masses of the vector bosons that mediate the weak interactions, of the quarks and of the charged leptons.

The discrete symmetries, in particular the parity and the particle–antiparticle conjugation operations and the corresponding quantum numbers.

An important dynamical symmetry of the hadrons, the invariance of the Lagrangian under rigid rotations in an ‘internal’ space, the isospin space. The unitary group is SU(2).

The notion of symmetry is essential in the determination of particle properties. It reveals quantities that are conserved in collisions or decays. It also constrains the mathematical formulation of theories. This chapter introduces these concepts and explains how the notion of symmetry is implemented in quantum mechanics. It reviews the quantities conserved in particle collisions or decays: energy-momentum and total angular momentum, and also the internal symmetries, such as parity, charge conjugation, baryon and lepton numbers.

Which of the four-parameter family of Friedman–Robertson–Walker (FRW) cosmological models best fits our universe and why? This chapter addresses these two central questions for observation and theory in cosmology. Of the four parameters that define an FRW model, only two are determined by observations so far: the Hubble constant; and the ratio of energy density in radiation to the critical density. To determine the others, the spacetime geometry of the universe must be measured on large scales through a study of how matter moves through it. We describe two illustrative ways of doing that – one based on observations of distant supernovae, and the other on observations of the cosmic background radiation. Remarkably, the best cosmological parameter values are consistent with the universe being spatially flat – right on the borderline between positive and negative spatial curvature.