Rest Mass Clarification I would like to know about the Rest Mass? 
Why we need the phrase "rest mass"? Because, mass is a constant quantity? Or Is the Mass varying with velocity? How can we understand that mass varying with velocity?
 A: "There is only one mass in Physics. The Mass." - Lev Okun
You are right. Mass is an invariant quantity that doesn't change with the change of frame. In special relativity, the momentum of a particle is given by $\displaystyle\frac{mv}{\sqrt{1-\Big(\displaystyle\frac{v}{c}\Big)^2}}$. Comparing this formula with the Newtonian momentum $mv$ led many people to think that in relativity the mass itself changes with velocity and its variation goes as $m=\displaystyle\frac{m_0}{\sqrt{1-\Big(\displaystyle\frac{v}{c}\Big)^2}}$. Where they called $m_0$ as the mass of the particle in its rest frame, or the rest mass. This formalism had some pseudo heuristic benefits including one of the major ideas that led Einstein to General Relativity but soon they started to realize that this definition has many theoretical troubles. The main two of them are as follows:


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*In the derivation of the relativistic momentum formula, it is clearly seen that the factor of $\sqrt{1-\Big(\displaystyle\frac{v}{c}\Big)^2}$ arises out of time dilation - a geometric effect and not from some structural change in the particle itself. So it is more logical to say that in relativity, the formula for the momentum changes and not the mass itself. As the factor $\sqrt{1-\Big(\displaystyle\frac{v}{c}\Big)^2}$ is not arising from any intrinsic characteristic of the particle. 

*If we chose Newton's $F=ma$ to give us the expression for the relativistic mass. Meaning that we would find a relativistic relation between the force and acceleration and then call the coefficient of acceleration as relativistic mass. Then we get two different expressions for mass in the case the force is acting normal to the velocity and the force is acting along the velocity. This clearly doesn't make any sense because mass is meant to denote properties inherent to the particle which we expect to not depend on the interrelation of its velocity and external force. 
Owing to such reasons, the concept of Relativistic mass is abandoned and now there is only one mass in Physics. Rest mass. Or better, Mass. 
Edit Eventually Einstein himself clearly discarded the idea of Relativistic Mass and made it clear that only logically consistent formalism of mass is in the terms of rest mass. 
