Intuitive

• The Concept of Mass by Lev Okun
• https://gravityandlevity.wordpress.com/2009/05/16/the-equivalence-of-mass-and-energy-the-center-of-energy/
• http://nautil.us/issue/54/the-unspoken/physics-has-demoted-mass
• Origins of Mass by Wilzeck

Concrete

See: The Concept of Mass by Okun

Abstract

• For a nice description see Mass in Quantum Yang-Mills Theory by L. D. Faddeev

In classical physics, mass is a conserved quantity, as has been experimentally demonstrated by Lavoisier (around 1790). In SR mass conservation is no longer valid—as has been shown in the 1930s by more accurate experimental techniques—and is superseded by energy-momentum conservation, as has been most vividly demonstrated in Alamogordo in 1945.Gauge Theory of Gravity and Spacetime by Friedrich W. Hehl

Why is it interesting?

A lower limit to the amount of energy that a particle can have is a property of a particle with a mass.An object may have any amount of kinetic energy, the amount getting smaller as the body slows toward rest. At this point the particle has its mini-mum energy; the amount of which, E, would then correspond to a mass m given by Einstein’s famous equation $E=mc^2$. For a massless body, the minimum energy in principle can be zero. From "The Infinity Puzzle", by Frank Close

FAQ

Can we explain masses in QFT?

QFT is not a theory which ”creates” masses of model-defining fields. The masses of those free fields which define the first order interaction density) are, together with the coupling strengths, free parameters5 . The only ”dynamic” masses are those of bound states created by acting with interacting composite fields on the vacuum state but unfortunately there is no perturbative methods which describes bound states. spacehttps://arxiv.org/pdf/1612.00003.pdf

What's the interpretation of mass in QFT?

see https://physics.stackexchange.com/questions/56903/the-interpretation-of-mass-in-quantum-field-theories