担任(工作等)；接受(任务等)；承担：
Who will undertake responsibility for this work?
谁将承担这项工作的责任?
此时undertake就相当于take，bear
.
负责；掌管：
I want you to undertake all the arrangements.
我希望你来负责全面安排工作。
此时undertake就相当于be in charge of
.
同意，答应；约定：
He undertook to finish the job by Wednesday.
他答应在星期三以前完成这项工作。
此时undertake to do相当于agree to do/consent to do sth.
2.
及物动词?If you?undertake?to?do something, you promise that you will do it. 承诺
例：
He undertook to edit the text himself.
他承诺亲自编辑正文。
此时相当于promise to do sth.