The 7-decays of levels in 26Mg have been investigated up to 12.5 MeV excitation energy by proton-7-ray coincidence measurements in the Z3Na(0~,pT) reaction at 14.2 and 16 MeV bombarding energy. Lifetime-measurements, made with the Doppler-shift attenuation method, and proton-7-ray angular-correlation measurements were performed at E,= 14.2 MeV. Many high-spin states were observed, among them levels at 6,978989(6 +) and 12,479(8 +, 7-) keV excitation energy. The spectrum of positive-parity states and their electromagnetic properties are reproduced with good accuracy by shell-model calculations which employ a unified s-d shell Hamiltonian and the unrestricted configuration space of the 0ds/2-1s1/2-0d3/~ shell. Members of five inferred rotational bands, with K~= 0 +, 2 +, 3 +, 0 + and 3-have been observed up to at least I= 6. The K~= 2 + band shows strong anomalies of excitation energies and E2 transition rates near the I= 6 state. The static intrinsic quadrupole moments calculated from the shell model wave functions indicate transitions from prolate to oblate deformation within the K~= 2 + band and also the ground state band. The lowest lying U =4 +. state appears to be "spherical" and cannot be associated with a rotational band.