Longman Dictionary of Contemporary English homepage

undertake

 verb
     
un‧der‧take W3 past tense undertook past participle undertaken [transitive] formal
1 to accept that you are responsible for a piece of work, and start to do it
undertake a task/a project/research/a study etc
Dr Johnson undertook the task of writing a comprehensive English dictionary.
2

undertake to do something

to promise or agree to do something:
He undertook to pay the money back in six months.
Definition from the Longman Dictionary of Contemporary English
Advanced Learner's Dictionary.

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