The Collaborative International Dictionary of English v.0.48:

Pursue \Pur*sue"\, v. i.
   1. To go in pursuit; to follow.
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            The wicked flee when no man pursueth. --Prov.
                                                  xxviii. 1.
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            Men hotly pursued after the objects of their
            ambition.                             --Earle.
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   2. To go on; to proceed, especially in argument or discourse;
      to continue.
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   Note: [A Gallicism]
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               I have, pursues Carneades, wondered chemists
               should not consider.               --Boyle.
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   3. (Law) To follow a matter judicially, as a complaining
      party; to act as a prosecutor. --Burrill.
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The Collaborative International Dictionary of English v.0.48:

Pursue \Pur*sue"\, v. t. [imp. & p. p. Pursued; p. pr. & vb.
   n. Pursuing.] [OE. pursuen, porsuen, OF. porsivre,
   poursuivre, poursuir, F. poursuivre, fr. L. prosequi; pro
   forward + sequi to follow. See Sue, and cf. Prosecute,
   Pursuivant.]
   1. To follow with a view to overtake; to follow eagerly, or
      with haste; to chase; as, to pursue a hare.
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            We happiness pursue; we fly from pain. --Prior.
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            The happiness of men lies in purswing,
            Not in possessing.                    --Longfellow.
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   2. To seek; to use or adopt measures to obtain; as, to pursue
      a remedy at law.
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            The fame of ancient matrons you pursue. --Dryden.
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   3. To proceed along, with a view to some and or object; to
      follow; to go in; as, Captain Cook pursued a new route;
      the administration pursued a wise course.
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   4. To prosecute; to be engaged in; to continue. " Insatiate
      to pursue vain war." --Milton.
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   5. To follow as an example; to imitate.
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   6. To follow with enmity; to persecute; to call to account.
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            The servant is not greater than his lord. If they
            have pursued me, they shall pursue you also.
                                                  --Wyclif (John
                                                  xv. 20).
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   Syn: To follow; chase; seek; persist. See Follow.
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WordNet (r) 3.0 (2006):

pursue
    v 1: carry out or participate in an activity; be involved in;
         "She pursued many activities"; "They engaged in a
         discussion" [syn: prosecute, engage, pursue]
    2: follow in or as if in pursuit; "The police car pursued the
       suspected attacker"; "Her bad deed followed her and haunted
       her dreams all her life" [syn: pursue, follow]
    3: go in search of or hunt for; "pursue a hobby" [syn: quest
       for, go after, quest after, pursue]
    4: carry further or advance; "Can you act on this matter soon?"
       [syn: pursue, follow up on, act on]