From the Latin "gradus" meaning "step, degree, rank":
* Graduate: To complete a course of study, typically at a college or university.
* Graduation: The act or ceremony of completing a course of study.
* Gradual: Happening or developing slowly over time.
* Grade: A level of academic achievement or quality; a step or stage in a process.
* Gradient: The rate of change of a variable over distance.
* Graduation: The act or ceremony of completing a course of study.
From the Latin "gradior" meaning "to walk, to step":
* Egress: The act or state of going out; an exit.
* Ingress: The act or state of going in; an entrance.
* Progress: The act or process of moving forward or developing.
* Regress: To go back to a previous state or condition.
* Degrade: To lower in rank, quality, or value.
Other related words:
* Degradation: The process of deteriorating or being broken down.
* Upgrade: To improve or enhance something.
* Downgrade: To lower in value or importance.
* Gradation: A series of gradual changes or steps.
This list isn't exhaustive, but it provides a good starting point for understanding the various ways "grad" can be used in English words.