Inertia is the resistance of any physical object to a change  in its state of motion or rest, or the tendency of an object to resist  any change in its motion. The principle of inertia is one of the  fundamental principles of 
classical physics which are used to describe the 
motion of 
matter and how it is affected by applied 
forces. Inertia comes from the Latin word, 
iners, meaning idle, or lazy. 
Isaac Newton defined inertia as his first law in his 
Philosophiæ Naturalis Principia Mathematica, which states:
[1]
  The vis insita, or innate force of matter,  is a power of resisting by which every body, as much as in it lies,  endeavours to preserve its present state, whether it be of rest or of  moving uniformly forward in a straight line.
In common usage the term "inertia" may refer to an object's "amount  of resistance to change in velocity" (which is quantified by its mass),  or sometimes to its 
momentum,  depending on the context. The term "inertia" is more properly  understood as shorthand for "the principle of inertia" as described by  Newton in his 
First Law of Motion;  that an object not subject to any net external force moves at a  constant velocity. Thus an object will continue moving at its current 
velocity until some force causes its speed or direction to change.
....
Interpretations 
 Mass and inertia 
 Physics and 
mathematics  appear to be less inclined to use the popular concept of inertia as "a  tendency to maintain momentum" and instead favor the mathematically  useful definition of inertia as the measure of a body's resistance to  changes in velocity or simply a body's inertial mass.
 This was clear in the beginning of the 20th century, when the 
theory of relativity was not yet created. Mass, 
m,  denoted something like an amount of substance or quantity of matter.  And at the same time mass was the quantitative measure of inertia of a  body.
 The mass of a body determines the momentum 

 of the body at given velocity 

; it is a proportionality factor in the formula:
 

 The factor 
m is referred to as 
inertial mass.
 But mass, as related to the 'inertia' of a body, can also be defined by the formula:
 

 Here, 
F is force, 
m is mass, and 
a is acceleration.
 By this formula, the greater its mass, the less a body accelerates under given force. Masses 

  defined by formula (1) and (2) are equal because formula (2) is a  consequence of formula (1) if mass does not depend on time and velocity.  Thus, "mass is the quantitative or numerical measure of body’s inertia,  that is of its resistance to being accelerated".
 This meaning of a 
body's inertia therefore is altered from the  popular meaning as "a tendency to maintain momentum" to a description  of the measure of how difficult it is to change the velocity of a body.  But it is consistent with the fact that motion in one reference frame  can disappear in another, so it is the change in velocity that is  important.
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