Virtual memory is, among other things, an abstraction to give the programmer the illusion of having infinite memory available on their system.
Virtual memory mappings are made to correspond to actual physical addresses. The operating system creates and deals with these mappings - utilizing the page table, among other data structures to maintain the mappings. Virtual memory mappings are always found in the page table or some similar data structure (in case of other implementations of virtual memory, we maybe shouldn't call it the "page table"). The page table is in physical memory as well - often in kernel-reserved spaces that user programs cannot write over.
Virtual memory is typically larger than physical memory - there wouldn't be much reason for virtual memory mappings if virtual memory and physical memory were the same size.
Only the needed part of a program is resident in memory, typically - this is a topic called "paging". Virtual memory and paging are tightly related, but not the same topic. There are other implementations of virtual memory, such as segmentation.
I could be assuming wrong here, but I'd bet the things you are finding hard to wrap your head around have to do with specific implementations of virtual memory, most likely paging. There is no one way to do paging - there are many implementations and the one your textbook describes is likely not the same as the one that appears in real OSes like Linux/Windows - there are probably subtle differences.
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