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A number of interesting theorems have recently been added to the existing ones in the field of integral transforms. The new arrivals can be broadly classified under two categories. The first expresses relationship between images and originals of related functions in the transforms concerned while the second reveals interconnections existing between images of related functions in the respective transforms. An attempt has been made in this paper to unify and extend all such results by establishing two most general theorems, embracing each of the two types mentioned above, and of elucidate their basic underlying principle. Certain special cases of these theorems which are of interest in themselves and do not seem to be recorded in the literature have also been given. Exact reference to twenty four theorems which follow as simple special cases of our theorems has also been given.