die Realisierung
implementation
The implementation or realization of an idea, plan, or project in practice.
Die Realisierung des neuen Stadtparks wird mehrere Jahre dauern.
The implementation of the new city park will take several years.

realization / implementation
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implementation
The implementation or realization of an idea, plan, or project in practice.
Die Realisierung des neuen Stadtparks wird mehrere Jahre dauern.
The implementation of the new city park will take several years.

Careful: The main meaning of 'Realisierung' (implementation/realization) in German is the implementation of a plan. The meaning 'Erkenntnis' (realization), as in English 'realization', is less common and often formal. In everyday language, 'Erkenntnis' (realization/insight) or 'das Begreifen' (understanding) is more likely to be used for this.
Die Realisierung der neuen Brücke ist unser wichtigstes Ziel.
The implementation of the new bridge is our most important goal.
'Realisierung' (realization/implementation) is derived from the verb 'realisieren' (to realize/implement). The ending '-ung' forms a feminine noun that describes the process or result of the action.
Wir müssen den Plan erst vollständig ausarbeiten, bevor wir ihn realisieren können.
We first have to work out the plan completely before we can implement it.
In the meaning 'Umsetzung' (implementation), 'Realisierung' (implementation/realization) is often combined with plans or projects. Typical phrases are 'die Realisierung eines Vorhabens' (the implementation of a project), 'an der Realisierung arbeiten' (to work on the implementation), or 'die Realisierung unterstützen' (to support the implementation).
Viele Freiwillige halfen bei der Realisierung des neuen Spielplatzes.
Many volunteers helped with the implementation of the new playground.
When 'Realisierung' (realization) describes an insight or realization, it is often followed by a subordinate clause with 'dass' (that). This structure explains exactly what was understood.
Die Realisierung, dass er einen großen Fehler gemacht hatte, war schmerzhaft.
The realization that he had made a big mistake was painful.
The meaning 'Umwandlung in Geld' (conversion into money) is technical language from business and finance. For example, people speak of the 'Realisierung von Gewinnen' (realization of gains) or the 'Realisierung von Vermögenswerten' (realization of assets).
Der Investor wartet auf den richtigen Zeitpunkt für die Realisierung seiner Gewinne.
The investor is waiting for the right time to realize his gains.
implementation / conversion
'die Umsetzung' and 'die Realisierung' both describe a plan or idea becoming something real. 'Umsetzung' often sounds more practical and emphasizes the steps taken to make it happen. 'Realisierung' sounds somewhat more formal and puts more emphasis on the result: something becomes possible and is actually done. The words can easily be confused because they are often used similarly in project-related texts. In everyday language, 'Umsetzung' is often more natural; for larger projects or official texts, you also often hear 'Realisierung'.

Die Realisierung des neuen Sportplatzes beginnt im nächsten Frühjahr.
The implementation of the new sports field will begin next spring.
Für die Umsetzung des Projekts brauchen wir klare Aufgaben.
For the implementation of the project, we need clear tasks.