apt command:

list:

[--installed], [--upgradeable], [--all-versions]

list packages based on package names.list is somewhat similar to dpkg-query --list in that it can display a list of packages satisfying certain criteria. 

search:

search in package descriptions

show:

show package details and information about the given package(s) including its dependencies, installation and download size, sources the package is available from, the description of the packages content and such more install, remove, purge: Performs the requested action on one or more packages specified via regex(7), glob(7) or exact match. The requested action can be overridden for specific packages by append a plus (+) to the package name to install this package or a minus (-) to remove it.

autoremove:

Remove automatically all unused packages that were automatically installed to satisfy dependencies for other packages and are now no longer needed as dependencies changed

update:

update list of available packages

upgrade:

upgrade the system by installing/upgrading packages

full-upgrade:

upgrade the system by removing/installing/upgrading packages

edit-sources:

edit the source information file (edit your sources.list)