teach
The word 'lehren' is used in German to express the act of teaching. It can be used in various contexts, such as teaching a subject, teaching a skill, or teaching a lesson. For example, 'Ich lehre Englisch' means 'I teach English'.
I teach mathematics at a university.
This sentence describes a person's occupation where they teach or instruct (lehre) a subject, in this case mathematics, at an institution, specified here as a university. Using 'lehre' indicates the speaker themselves are the one doing the teaching. The object, which is what is being taught, follows the verb.
He can teach guitar well.
In this situation, the verb 'lehren' describes the ability of a person (in this case, 'er' or 'he') to teach or give instruction in an area or on a topic, specified here as 'gitarre' or 'guitar'. Note that the auxiliary verb 'kann' (can) is used to express the person's capability to do the action.
Should I teach you German?
This sentence is a question where the speaker is asking if he or she should teach ('lehren') the listener German. 'Dir' (to you) is the indirect object of the sentence, meaning the teaching is being done to 'you'. The verb 'soll' (should) is used to ask for permission or suggest the action.