buchen
to book
To reserve or buy something in a binding way, for example a flight, a hotel room, or a ticket.
Wir haben für den Sommer eine Reise nach Italien gebucht.
We booked a trip to Italy for the summer.

to book
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to book
To reserve or buy something in a binding way, for example a flight, a hotel room, or a ticket.
Wir haben für den Sommer eine Reise nach Italien gebucht.
We booked a trip to Italy for the summer.

The verb 'buchen' (to book/post) is closely related to 'das Buch' (book). Originally, it meant entering something into a book. This origin can still be seen today in accounting, when a business transaction is recorded.
Früher wurden alle Einnahmen von Hand in ein großes Buch gebucht.
In the past, all income was posted by hand in a large book.
You can tell from context whether 'buchen' means 'to reserve' or 'to record in accounting.' Words like 'Reise' (trip), 'Flug' (flight), or 'Hotel' (hotel) point to a reservation, while 'Rechnung' (invoice), 'Konto' (account), or 'Betrag' (amount) refer to accounting.
Ich habe online einen Flug nach Berlin gebucht.
I booked a flight to Berlin online.
In everyday life, 'buchen' is very often used in fixed combinations. Typical phrases are: 'einen Flug buchen' (to book a flight), 'ein Hotelzimmer buchen' (to book a hotel room), 'eine Reise buchen' (to book a trip), or 'Tickets für ein Konzert buchen' (to book tickets for a concert).
Wir sollten die Tickets für das Musical frühzeitig buchen.
We should book the tickets for the musical early.
In the context of accounting, the preposition 'auf' is often used to indicate where something is posted. You post an amount to a specific account.
Bitte buchen Sie diese Ausgabe auf das Konto für Büromaterial.
Please post this expense to the office supplies account.
When something is mentally classified, 'buchen' is often used with the preposition 'als' (as) and an accusative object. You count something as a success or as an experience.
Den knappen Sieg konnte die Mannschaft als großen Erfolg buchen.
The team could count the narrow victory as a great success.
to buy
'kaufen' and 'buchen' both have to do with paying for something or getting something in a binding way. You generally use 'kaufen' when you get an object in exchange for money, for example clothes, food, or a bicycle. You use 'buchen' especially for trips, appointments, courses, hotels, flights, or tickets. This often involves a reservation or a service for a specific time. Learners may confuse the words because you pay money in both cases. A simple rule is: you buy things, but you often book trips and seats.

Für den Sommer buchen wir heute die Zugtickets nach Hamburg.
Today we are booking the train tickets to Hamburg for the summer.
Elif kauft am Montag ein neues Notizbuch für den Deutschkurs.
Elif buys a new notebook for the German course on Monday.