A conservation law is nothing but a statement that a particular quantity (energy, momentum etc.) stays constant during a process. There are at least 6 different conservation laws encountered in Physics, as follows:
Conservation of Mass
This law states that in any non-relativistic chemical or physical process(except nuclear processes), the total mass of an isolated system stays constant. In relativistic situations (and nuclear processes) mass is seen as a manifestation of energy associated with matter. In that case we consider the conservation of energy only and mass is represented by “mass energy“.
Conservation of Energy
The most popular of them all. It states that the total energy of an isolated system (including kinetic energy, potential energy, mass energy etc.) is the same before and after it undergoes a process. By isolated system we mean that it does not interact with its surroundings in any manner. Since the Universe as a whole is an isolated system(as far as we can say), the total energy of itself must be constant as well.
This law appears in many forms in different branches of Physics, e.g. as the first law of thermodynamics or as work-energy theorem in mechanics.
Conservation of Linear Momentum
Conservation of Angular Momentum
Analogous to the law of conservation of linear momentum, this one states that the total angular momentum of a system stays constant if no external torque act on it. (Torque ≡ moment of force)
Conservation of Charge
Electric charge is a fundamental properties of particles. Any particle which carries charge is either positively charged or negatively charged. e.g. protons carry net positive charge of 1 while electrons have -1. The law states that in any particle interaction, the net electric charge stays constant.
Consider the following decay of a pion into a muon and muon neutrino:
Total charge on the left hand side = +1(on pion)
Total charge on the right hand side = +1(muon)+0(neutrino) = +1
Hence, total charge is conserved.
Conservation of Baryon Number
Baryons are a kind of fundamental particles such as protons and neutrons. Each of them has been assigned a particular Baryon Number(Baryons have +1 and antibaryons have -1, rest of the particles are assigned 0). The law states that in any particle interaction(strong, weak, electromagnetic or gravitational), the net Baryon number before and after the interaction remains unchanged.
Consider the following process:
Baryon number on left hand side =o(pion) +1(proton)
Baryon number on the right hand side = +1(lambda)+o(Kaon)
Clearly, both baryon number and electric charge are conserved.
Conservation of Lepton Number
Elementary particles such as electrons, neutrinos etc(and their antiparticles) are known as Leptons. Just like Baryons, each of the Leptons has been assigned a Lepton Number(e.g. electrons have +1). The particles which are not leptons are assigned a lepton number of 0. The law states that the net Lepton number before and after a particle interaction stays constant.
e.g. consider the process of neutron decay:
Lepton number on left hand side = 0(neutron)
Lepton number on right hand side = 0(proton)+1(electron)-1(electron antineutrino)
Clearly, Lepton number is conserved in this process. Note that the Baryon number and electric charge are conserved as well.