"A measurement of the 2S-2P transition frequencies (Lamb shift) in the muonic helium-3 and 4 ions by means of laser spectroscopy is proposed. This will lead to a ten times more accurate determination of the root-mean-square (rms) charge radii of the He-3 and He-4 nuclei. The radius of the magnetic moment distribution inside the He-3 nucleus will result from the hyperfine structure in muonic 3He.In the muonic helium ion, a single negative muon orbits the helium nucleus. The muon is a point-like lepton, just as the electron, except it is about 200 times heavier. This gives a factor of 200^3 = 10^7 enhancement of nuclear finite size effects on the energy levels of muonic vs. regular (electonic) Helium ions. Muonic helium is the ideal sytem to study the He nuclear size.The CREMA project has four main aims:(1) Solve the ""proton size puzzle"" created by our recently completed muonic hydrogen project [R. Pohl et al., ""The size of the proton"", Nature 466, 213 (2010)]. Our tenfold improvement of the proton charge radius resulted in a five sigma discrepancy with the 2006 CODATA value, which is mostly based on hydrogen spectroscopy. This poses a serious challenge to bound-state QED, and may even point towards new physics. CREMA will help to clarify this.(2) Absolute nuclear charge radii of all helium isotopes He-3,4,6,8 will result from CREMA. The charge radius differences are precisely known, but the absolute size of the He-4 anchor nucleus can best be measured in muonic helium. Absolute charge radii are a more stringent benchmark for few-nucleon nuclear models than the radius difference.(3) Test of bound-state QED: Spectroscopy of regular He+ ions is underway. He+ (Z=2) is more sensitive than hydrogen (Z=1) to higher-order QED contributions which scale as Z^5. An accurate He charge radius from CREMA is mandatory for this.(4) An improved value of the Rydberg constant will result from the He+ spectroscopy only with the improved charge radius from CREMA."