Synonyms for Undertake:

n.

consent, yield, say yes, go along with, accede, commit yourself. shoulder, swear, vow, vouchsafe, incur, give (someone) your word. obligation, pledge, promise, agree. enter, open, take up, lead off, set-to, get off, launch, institute, kick off. undertake (noun)
contract, take on, tackle, set about, take in charge, attempt, guarantee.

v.

attempt, engage in (verb)
commence, set in motion, take upon oneself, offer, initiate, endeavor, launch, agree, move, volunteer, go in for, contract, begin, stake, answer for, shoulder, promise, set about, go into, take on, guarantee, venture, try out, embark, take the plunge, tackle, fall into, commit, pledge, hazard.
begin (verb)
bud, form, inaugurate, prepare, emerge, dawn, conceive, spring, introduce, embark, induct, start, hatch, sprout, originate, commence, create, initialize, stem, begin, develop, birth, germinate.
creation (verb)
set about, attempt.
endeavor (verb)
volunteer, act, assay, attempt, endeavor, proceed, aim, engage, commit, perform, venture, maneuver, contract, exploit, approach.
pursue (verb)
dog, aspire, quest, chase, sleuth, harry, seek, track, intend, search, hunt, follow, trail, tail, strive, stalk.
venture (verb)
initiate, pursue, scheme, campaign.

Other synonyms:

consent, vow, go along with, agree. go into, incur, promise, pledge, accede, swear. yield, launch. shoulder, institute. enter. act
go in for.
approach
set about.
begin
initiate, introduce, set in motion, approach.
carry out
DO.
contract
go along with.
go into
take upon oneself.
set about
fall to, set about.
tackle
embark upon.
take on
address oneself to.
Other relevant words:
enter, vouchsafe, consent, take upon oneself, tackle, institute, pledge, lead off, fall into, embark upon, accede, kick off, set in motion, address oneself to, vow, open, incur, try out, offer, move, answer for, go in for, set about, launch into, hazard, swear, promise, take the plunge, agree, go into, get off, stake, launch, launch forth, take on, take in charge, buckle to, devote oneself to, shoulder, fall to, pitch into, guarantee.

Usage examples for undertake

  1. Do you undertake the task at once. – Beric the Briton A Story of the Roman Invasion by G. A. Henty
  2. Why do I undertake such an employment as this? – Basil by Wilkie Collins
  3. Well, didn't you undertake to teach me how last evening? – Mr. Marx's Secret by E. Phillips Oppenheim