das Kapitel
chapter
A section in a book or another longer text, usually numbered or provided with a heading.
Lies bitte für morgen das dritte Kapitel.
Please read the third chapter for tomorrow.

chapter
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chapter
A section in a book or another longer text, usually numbered or provided with a heading.
Lies bitte für morgen das dritte Kapitel.
Please read the third chapter for tomorrow.

The meaning 'stage of life' is a metaphor. Life is seen like a book in which you begin new chapters or close old ones. This idea helps you understand the figurative meaning.
Nach der Trennung war es Zeit, ein neues Kapitel aufzuschlagen.
After the breakup, it was time to open a new chapter.
The idiom 'ein Kapitel für sich sein' (to be a chapter of its own) describes a topic that is so complicated or special that it has to be treated separately. The subject is the complex topic itself.
Die Steuererklärung ist jedes Jahr wieder ein Kapitel für sich.
The tax return is a chapter of its own every year.
In the metaphorical meaning, 'Kapitel' (chapter) is often combined with verbs such as 'beginnen' (to begin), 'aufschlagen' (to open, meaning to start something new), or 'abschließen' (to close, meaning to end something).
Mit seiner Pensionierung schloss er ein langes berufliches Kapitel ab.
With his retirement, he closed a long professional chapter.
When talking about a book, 'Kapitel' (chapter) is almost always used with an ordinal number (first, second, third...) to indicate the position in the text.
Die Lösung für das Rätsel finden Sie im letzten Kapitel.
You will find the solution to the puzzle in the last chapter.
part
'der Teil' and 'das Kapitel' both refer to a section of something larger. 'der Teil' is very general: a part can belong to a text, an object, a plan, or a quantity. 'das Kapitel' is more specific and is used mainly for books or longer texts. It can also figuratively mean a phase in life or in a development. Learners may confuse the words when talking about texts. In a book, a chapter is a specific section of text; 'Teil' remains more general and can also include several chapters.

Für die Prüfung liest Sofia heute noch das dritte Kapitel im Lehrbuch.
For the exam, Sofia is still reading the third chapter in the textbook today.
Den letzten Teil des Films habe ich nicht verstanden.
I didn't understand the last part of the film.