A promise is a statement in which you that you will do something or not do something. "I promise to be on time." "I promise not to forget you birthday next time." If you pledge something, it is more solemn. Alcoholics when they stop drinking will take an official pledge to stop drinking. It is also a commitment to do something, such as pledging a contribution to a charity. If I pledge a donation, it means that I will make the donation later. It is not considered solemn. If you swear something, it can be a promise or a pledge, but usually refers to a person officially stating that what they say is true. People called to testify in a court must first swear that what they will say is the truth.