chase

追う(おう)	Chase – not just cat chases mouse, but also can mean to chase someone in a certain direction, for instance, to drive someone off, or to herd cattle.

追求(ついきゅう)	To pursue, usually used figuratively (pursue justice, pursue happiness, pursue a career)

追いかける(おいかける)	To chase after – Like a cop chasing a crook. A more narrow meaning than just 追う. $$$

追いつく(おいつく)	Catch up to.

追越す(おいこす)	Overtake.