sich aneignen
to acquire
To learn a skill, knowledge, or a particular behavior, usually through one's own effort.
Sie hat sich in kurzer Zeit sehr gute Spanischkenntnisse angeeignet.
She acquired very good Spanish skills in a short time.

to acquire / appropriate
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to acquire
To learn a skill, knowledge, or a particular behavior, usually through one's own effort.
Sie hat sich in kurzer Zeit sehr gute Spanischkenntnisse angeeignet.
She acquired very good Spanish skills in a short time.

'Aneignen' (to acquire / appropriate) is a separable verb. The prefix 'an-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er eignet sich schnell neue Fähigkeiten an.
He quickly acquires new skills.
The verb is always reflexive and requires the reflexive pronoun in the dative. What one acquires or appropriates is in the accusative. So the structure is: person (subject) + eignet + sich (dative) + something (accusative) + an.
Ich eigne mir gerade die Grundlagen der Programmierung an.
I am currently acquiring the basics of programming.
The meaning depends on the object. If it is abstract knowledge or skills ('eine Sprache' (a language), 'eine Methode' (a method)), it means 'erlernen' (to learn/acquire). If it is concrete property or rights ('Land' (land), 'Vermögen' (wealth)), it means 'unrechtmäßig nehmen' (to take unlawfully).
Sie hat sich einen neuen Arbeitsstil angeeignet.
She acquired a new working style.
In the meaning 'erlernen' (to learn/acquire), the verb is often combined with abstract nouns. Typical collocations are: 'sich Wissen aneignen' (to acquire knowledge), 'sich Fähigkeiten aneignen' (to acquire skills), 'sich Kenntnisse aneignen' (to acquire knowledge/skills), or 'sich eine Gewohnheit aneignen' (to acquire a habit).
Im Laufe der Jahre hat er sich ein enormes Fachwissen angeeignet.
Over the years, he acquired enormous specialist knowledge.
The meaning 'unrechtmäßig nehmen' (to take unlawfully) is used mainly in a formal, legal, or historical context. In everyday language, you would be more likely to use other verbs.
Historische Texte beschreiben, wie sich der Adel Ländereien aneignete.
Historical texts describe how the nobility appropriated lands.
to learn
'lernen' and 'sich aneignen' can both mean that you acquire new knowledge or a new skill. 'lernen' is the general and very normal word: you learn at school, in a course, or through practice. 'sich aneignen' places more emphasis on your own active effort and sounds somewhat more formal. It is often used with knowledge, skills, or habits. Learners may confuse the words because their meanings are similar. The form is also important: in this meaning, you say 'sich etwas aneignen' (to acquire something).

Im neuen Job eignet sich Anna viele technische Kenntnisse an.
In her new job, Anna is acquiring a lot of technical knowledge.
Für die Prüfung lernt Mehmet jeden Abend eine Stunde.
Mehmet studies for an hour every evening for the exam.