RPMs jump between gears and while idling

What is your question?

I'm not sure if I used the correct terminology, but when I turn on my car the RPMs warm-up around 1,500. Then I start driving and while my car is shifting into the next gear the RPMs shoot up until it finally hits the next gear and continues on normally. At this point if I were to park, my RPMs would rev up to 2,500 then back down to 1,000 and continue to go back and forth until I shifted back into drive or turned the car off. Hope this makes sense. Any help would be greatly appreciated!