aufbauen
to assemble / set up
To physically erect something or put it together from individual parts.
Wir haben das Zelt in nur zehn Minuten aufgebaut.
We set up the tent in just ten minutes.

to build up
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to assemble / set up
To physically erect something or put it together from individual parts.
Wir haben das Zelt in nur zehn Minuten aufgebaut.
We set up the tent in just ten minutes.

'Aufbauen' (to build up) is a separable verb. The prefix 'auf-' comes at the end of the sentence in main clauses, but remains attached to the verb in subordinate clauses. In the infinitive with 'zu', 'zu' comes between the prefix and the verb.
Mein Sohn baut gerade eine Burg aus Legosteinen auf.
My son is building a castle out of Lego bricks right now.
In the abstract meaning, 'aufbauen' (to build up) is often combined with concepts like trust, relationships, or structures. Typical phrases are 'Vertrauen aufbauen' (to build trust), 'ein Netzwerk aufbauen' (to build a network), or 'Druck aufbauen' (to build up pressure).
Es dauert lange, eine gute Freundschaft aufzubauen.
It takes a long time to build a good friendship.
When 'aufbauen' (to encourage) has a person as its object, it means to support or comfort that person emotionally. So the object is always a person or group that needs encouragement.
Nach dem verlorenen Spiel musste der Kapitän seine Mitspieler wieder aufbauen.
After the lost game, the captain had to encourage his teammates again.
In the meaning 'basieren auf' (to be based on), 'aufbauen' (to build on) is always used with the preposition 'auf' and the dative. The separable prefix 'auf-' comes at the end of the sentence.
Dieser Kurs baut auf den Grundlagen des letzten Semesters auf.
This course builds on the fundamentals from last semester.
To describe a structure or organization, 'aufbauen' (to structure) is very often used in the passive or as the past participle. The question for this is often: 'Wie ist etwas aufgebaut?' (How is something structured?)
Der Roman ist in drei Teile aufgebaut.
The novel is structured in three parts.
The reflexive form 'sich aufbauen' (to rise up) is often used for large, threatening natural phenomena or obstacles. It describes how something slowly becomes larger and more imposing.
Am Horizont bauten sich dunkle Gewitterwolken auf.
Dark thunderclouds rose up on the horizon.
to develop
'entwickeln' and 'aufbauen' can both describe something coming into being over time and becoming better or larger. 'entwickeln' emphasizes change and progress, for example with an idea, software, or a skill. A person or situation can also develop. 'aufbauen' places more emphasis on the foundation and structure: you create a system, relationship, organization, or text step by step. The words can be confused because both describe a process. As a guide: 'entwickeln' is more about how something becomes; 'aufbauen' is more about what something is based on and how it is organized.

Meine Kollegin baut eine neue Abteilung für Umweltfragen auf.
My colleague is building up a new department for environmental issues.
Mein Bruder hat im Kurs eine eigene Idee für ein kleines Spiel entwickelt.
In the course, my brother developed his own idea for a small game.