Question: On page 182 of the PHB there are rules describing how far and high characters can jump. However, there is no mention of what type of action jumping is or how much movement it takes to initiate a jump. In the combat chapter of the book there is no action listed that allows a character to attempt any sort of acrobatics or athletics in combat. Which leads me to think if it's even an option. **Can you jump in combat and if so what are the restrictions?**

In case it's important I was wondering about this when I came across the spell Jump. It simply triples the distance the target can jump and lasts 1 minute. If cast on a martial character with 20 Strength they could jump 60 feet. That kind of mobility could be useful in combat.

Answer: 
Per the rules for jumping in the Adventuring chapter (Basic Rules p64, probably the same section you cite):

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> each foot you clear on the jump costs a foot of movement.
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Yes, you can jump in combat as part of your movement; no, you can't jump further than you could move anyway. Rules as written, the Jump spell doesn't extend this distance.

If I were the GM, I would say that the Jump spell makes every three feet you clear cost a single foot of movement, but that would be a house ruling.
Jump is part of "Move."

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> Your movement can include jumping, climbing and swimming. These different modes of movement can be combined with walking, or they can constitute your entire move. However, you're moving, you deduct the distance of each part from your speed until it is used up or until you are done moving. (PHB 190)
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For distance traveled on Jump, you move your strength score (provided that you move at least 2 squares prior to your jump, otherwise it's half that). This movement still costs the normal amount for each foot of movement:

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> Either way, each foot you clear on the jump costs a foot of movement.
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So if a wizard casts Jump, your jump movement is still limited by your character's speed. However, this allows for a standing jump which means that you could jump 25 or 30' in a single move instead of 15-20'.