die Veröffentlichung
release / publication
The act of making a work, such as a book, film, music, or study, available to the public.
Die Band feierte die Veröffentlichung ihres neuen Albums.
The band celebrated the release of their new album.

publication / release
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release / publication
The act of making a work, such as a book, film, music, or study, available to the public.
Die Band feierte die Veröffentlichung ihres neuen Albums.
The band celebrated the release of their new album.

The word derives from the verb 'veröffentlichen' (to publish), which in turn is based on the adjective 'öffentlich' (public). A 'Veröffentlichung' (publication/release) is therefore literally the process of making something public.
Der Forscher möchte seine Ergebnisse bald veröffentlichen.
The researcher would like to publish his results soon.
Whether the act (m01) or the work (m02) is meant can be recognized from context. If the word refers to a point in time or an event ('nach der Veröffentlichung' — after the publication/release), the act is meant. If it appears in the plural or is counted ('drei Veröffentlichungen' — three publications), the work is meant.
Kurz nach der Veröffentlichung wurde das Buch zum Bestseller.
Shortly after its release, the book became a bestseller.
When the act of publishing is meant, the noun is often combined with the genitive of the work. Typical verbs are 'ankündigen' (to announce), 'verschieben' (to postpone), or 'feiern' (to celebrate).
Die Veröffentlichung des neuen Videospiels wurde auf nächstes Jahr verschoben.
The release of the new video game was postponed until next year.
expense / issue / output
'die Ausgabe' and 'die Veröffentlichung' can both have to do with books, newspapers, studies, or other works. An 'Ausgabe' is a specific version or individual issue of a work, for example the new issue of a newspaper. A 'Veröffentlichung' is either the moment when something is made public, or the published work itself. They can be confused because both occur in the context of publications. 'Ausgabe' fits when you mean a specific version; 'Veröffentlichung' fits when you are talking about making something public or about a published work in general.

Zur Veröffentlichung der Studie schickt sie morgen eine E-Mail an alle Kollegen.
For the publication of the study, she will send an email to all her colleagues tomorrow.
In der neuen Ausgabe der Zeitung steht ein Bericht über den Stadtpark.
The new issue of the newspaper has a report about the city park.