auswendig
by heart
To keep something in memory and be able to reproduce it without a text or aids; from memory.
Für das Theaterstück musste er eine lange Rede auswendig lernen.
For the play, he had to learn a long speech by heart.

by heart
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by heart
To keep something in memory and be able to reproduce it without a text or aids; from memory.
Für das Theaterstück musste er eine lange Rede auswendig lernen.
For the play, he had to learn a long speech by heart.

'Auswendig' (by heart) is most commonly combined with the verb 'lernen' (to learn). Other typical verbs are 'können' (to know/be able to), 'wissen' (to know), 'kennen' (to know), or 'aufsagen' (to recite).
Kannst du das Gedicht schon auswendig?
Do you already know the poem by heart?
As an adverb, 'auswendig' (by heart) usually stands at the end of a sentence or clause, directly before the conjugated verb or the past participle.
Sie hat ihre Präsentation komplett auswendig gelernt.
She learned her presentation completely by heart.
People typically learn things by heart that have a fixed form, such as 'ein Gedicht' (a poem), 'einen Text' (a text), 'Vokabeln' (vocabulary), 'eine Formel' (a formula), or 'eine Telefonnummer' (a telephone number).
Ich kenne ihre Telefonnummer nicht auswendig.
I don't know her telephone number by heart.
free
'frei' and 'auswendig' can both mean that you are not reading from a sheet of paper. The difference lies in the focus. 'auswendig' means that you have learned something beforehand and can reproduce it exactly from memory. In a presentation or when speaking, 'frei' means more that you speak without a fixed text and formulate things independently. So you can speak freely without having learned everything by heart. Learners may confuse the words because both work without a written prompt. 'auswendig' fits with poems, rules, or texts; 'frei' fits more with conversations, presentations, or your own formulations.

Für die Prüfung lernt Anna das kurze Gedicht auswendig.
Anna is learning the short poem by heart for the exam.
Im Kurs spricht Mehmet frei über sein Wochenende.
In the course, Mehmet speaks freely about his weekend.