A Cubism Reader by 
The Tradition of Constructivism by 
The Weimar Republic Sourcebook by 
Between Worlds by
Many pieces from key modernist journals have been translated and anthologised in book form. Some examples appear in the column to the left.
Other journals have been digitised for free online viewing:
Avant-garde and Modernist Magazines
Comprehensive guide to finding these magazines online, from the website Monoskop.
Gallica
Not just modernism: Gallica is a very large collection of books and other material uploaded by the Bibliothèque nationale de France. Almost all material is in French. However you can search for material in a specific language, and the website itself can be viewed in several different languages.
National Diet Library (Japan)
Digitised magazines and other historical material, relevant to studying modern Japanese art.
Ubuweb
May be less reliable in the information it provides, e.g. in the citations for articles, but is nevertheless worth investigating.
Exhibition catalogues
Ben Uri Gallery & Museum exhibition catalogues: focussed on Jewish and immigrant artists in Britain from 1900 onwards.
Guggenheim Publications
Online catalogues and other publications from the Solomon R.Guggenheim Museum.
MoMA exhibition catalogues
Database of catalogues and other exhibition documentation from MoMA.
Whitney Biennial
All catalogues up to 1995 online.
For contemporary press coverage of exhibitions and sales, see the guide to finding historic newspapers.