gründen
to found
To bring something new into being, especially a company, an organization, a city, or a family.
Sie plant, nächstes Jahr ihr eigenes Unternehmen zu gründen.
She plans to found her own company next year.

to found / be based on
Loading your saved state.
to found
To bring something new into being, especially a company, an organization, a city, or a family.
Sie plant, nächstes Jahr ihr eigenes Unternehmen zu gründen.
She plans to found her own company next year.

The verb 'gründen' (to found / be based on) is closely related to the noun 'der Grund' (the reason; the ground). This connection helps explain the meanings: you lay the 'Grundstein' (foundation stone) for a company (gründen = to found), an opinion is based on a 'Grund' (reason) (sich gründen auf = to be based on), or a ship touches the 'Meeresgrund' (seabed) (gründen = to run aground).
Der Erfolg der Firma gründet auf einer einfachen, aber genialen Idee.
The company's success is based on a simple but brilliant idea.
In its most common meaning, 'gründen' is combined with things that one brings newly into being. Typical examples are: eine Firma gründen (to found a company), einen Verein gründen (to found an association/club), eine Familie gründen (to start a family), or eine Organisation gründen (to found an organization).
Nach dem Studium wollen sie eine Familie gründen.
After their studies, they want to start a family.
In the meaning 'basieren auf' (to be based on), the verb is always reflexive and is used with the preposition 'auf' and the accusative. The structure is: Etwas gründet sich auf etwas (something is based on something).
Ihre Anklage gründet sich auf Zeugenaussagen.
Her accusation is based on witness statements.
The meaning 'mit dem Schiff auf Grund laufen' (to run aground with a ship) is technical language from seafaring. You hear or read this word only in this specific context.
Der Kapitän musste melden, dass sein Schiff im flachen Wasser gegründet war.
The captain had to report that his ship had run aground in shallow water.
to open
'gründen' and 'eröffnen' can both be used at the beginning of something, for example with a company or a shop. Use 'gründen' when something new is brought into being: a company, an organization, or a family. Use 'eröffnen' when something is made accessible for the first time or officially begun, for example a shop, an exhibition, or a meeting. Learners often confuse the words when talking about shops: you 'gründet' the company as a legal or organizational unit, but you 'eröffnet' the shop for customers.

Nach dem Studium möchte Lena eine kleine Firma gründen.
After her studies, Lena would like to found a small company.
Am Samstag eröffnet das neue Café in unserer Straße.
The new café on our street opens on Saturday.