I was told by my professor that ICs can be of two types, monolithic and hybrid and then she went on to explain technologies of fabrication. What is the difference between a monolithic IC and a hybrid IC?
A monlithic integrated circuit has the full circuit constructed on a single piece of silicon or other semiconductor, then (usually) enclosed in a package with connecting leads.
A Hybrid circuit consists of a (often ceramic) substrate carrying one or more silicon chips (which may themselves be monolithic integrated circuits, individual diodes, or transistors). Resistors and conductive tracks may be deposited on the substrate, and other parts may be soldered to the tracks to form a complete circuit. A hybrid can also use mixed technology, such as GaSs chips along with silicon chips.
I would not normally consider a hybrid to be a type of integrated circuit, but others might.