I suspect this is a mistranslation of German bzw. = beziehunsweise, which can mean either respectively or or as the case may be. The translator has taken a passage in which the latter sense is intended and substituted the conventional abbreviation of the former sense.

The latter sense has no convenient one-word English translation, much less an abbreviation. I have often regretted this, because bzw. is so useful.

It sort of works, but not so gracefully, if you just substitute or for resp.

For each of these problems (or tools), we start by presenting the natural concern underlying it (or its intuitive objective), then define the problem (or tool), and finally demonstrate that the problem can be solved (or the tool can be constructed).

I suspect this is a mistranslation of German bzw. = beziehungsweise, which can mean either respectively or or as the case may be. The translator has taken a passage in which the latter sense is intended and substituted the conventional abbreviation of the former sense.

The latter sense has no convenient one-word English translation, much less an abbreviation. I have often regretted this, because bzw. is so useful.

It sort of works, but not so gracefully, if you just substitute or for resp.

For each of these problems (or tools), we start by presenting the natural concern underlying it (or its intuitive objective), then define the problem (or tool), and finally demonstrate that the problem can be solved (or the tool can be constructed).