Can there be friction unless the objects in contact are not acted upon by an external force? The definition of friction I read from The book, General Physics written by Henry Crew is that, The resistance which either one of the body offers to the motion is called force of friction". If it is produced only while motion according to definition then can there be friction when two surfaces are in contact and not move relative to each other?
 A: Friction acts on objects at rest too . The definition meant that if there is relative motion between two objects then friction will act as a resistance between them . If you find two objects at rest even when an external force is applied on it then it means friction is acting on them . Had there been no friction there would have been relative motion and the definition means that this motion will be opposed by friction ( if it happens to exist ) .   

In the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion.  

This was on Wikipedia
A: The resistance to motion can also occur when the object is at rest.   I push on a book, and it doesn't yet move.  The object is not in motion, so there must be force that balances my push.  That force, which is resisting motion, is friction.
When the two objects are in relative motion we call it kinetic friction.  When they are at rest relative to one another, it's static friction.
A: when two objects are in contact with each other and are at rest, then the friction force is zero, because the direction of friction force is always parallel to the surface of contact, and when the two bodies are in contact and also at rest than only two forces act on the body i:e, weight of the body which is downward and the normal force which is upward, there is no other force which is parallel to the surface of contact. 
at this stage only the magnitude of friction force exist and is also maximum, numerically equal to coefficient of static friction times the normal force.  
A: there will be friction but not frictional force will exist because surface will still be interlocked when the object is not moving but if FRICTION FORCE existed then from the direction in which it is acting ,the object will come in motion due to effect of force 
