(scroll down for UK opportunities)
HdA’s International Summer Internship Programme – The Haus der Astronomie in Heidelberg, Germany offers three week internships for those older than 16 but haven’t yet started University.
Leiden/ESA – One of the most prestigious summer programmes out there, Leiden University offers a fantastically comprehensive list of research topics.
ASTRON/JIVE – Located in the Netherlands at the Dwingeloo Observatory, with a focus on Radio Astrophysics, there is still a great range of topics available to carry out research on.
MPIA – Summer internships available at the Max Planck Institute near Heidelberg. They last 1-3 months around summer time, with a salary of about €1000 a month.
IAC – This funded summer grants programme takes place on the Canary Islands with projects in astrophysics or technology.
INT – The Isaac Newton Group of Telescopes offers a year long Studentship for those who are currently undergraduate, Masters or PhD students, on La Palma.
MultiDark – The University of Valencia offers a Student Summer Programme for those in their final year of a Bachelors and interested in Dark Matter Detection.
Padova – The Astronomical Observatory in Padova offers some projects (scroll down for projects in English).
NCAC – The Nicolaus Copernicus Astronomical Centre offers the chance to carry out scientific research in Warsaw and Torun, Poland.
RISE – Limited to students from the UK, US and Canada, there are always opportunities to carry out Astrophysical research at choice of different German institutions.
ESO – The European Southern Observatory usually have internships available throughout the year, often in Garching, Germany.
Young Graduate Trainees – A fantastic one year opportunity for Masters graduates to work at ESA, for nationals of ESA Member States and Cooperating States. And they’ve just reopened applications too (until end of Jan 2016)!
Also see the National Trainee Programmes.
CERN – Because, well, CERN.
UCL – 5 scholarships are available for international students this year with many different research themes available, for a 2 month period. They also don’t mind if you have funding from elsewhere. Here is the Astrophysics department page.
UROP – The Undergraduate Research Opportunities Programme at Imperial College London is also available to Masters students, and has a couple of Astrophysics research topics available.
Oxford – Summer Research Programme for EU nationals.
SURE – Limited to students studying in the UK, undertake research within the Department of Physics and Astronomy and the Space Research Centre at the University of Leicester.
STFC – The Science and Technology Facilities Council provide the chance for UK undergrads to work at The UK Astronomy Technology Centre in Edinburgh.
Cardiff – Cardiff University offer the Leonid Grishchuk Summer Internship in Gravitational Physics each summer. You will get £275 per week, open to any undergraduate student of the world.
King’s – Internships available for up to three months in Cosmology, at King’s College London. Unfortunately no funding available, but you can always apply to other trusts and things.