  We present results from and the analysis of data from MAXIPOL, a
balloon-borne experiment designed to measure the polarization in the Cosmic
Microwave Background (CMB). MAXIPOL is the first CMB experiment to obtain
results using a rotating half-wave plate as a rapid polarization modulator. We
report results from observations of a sky area of 8 deg^2 with 10-arcmin
resolution, providing information up to l~700. We use a maximum-likelihood
method to estimate maps of the Q and U Stokes parameters from the demodulated
time streams, and then both Bayesian and frequentist approaches to compute the
EE, EB, and BB power spectra. Detailed formalisms of the analyses are given. A
variety of tests show no evidence for systematic errors. The Bayesian analysis
gives weak evidence for an EE signal. The EE power is 55^{+51}_{-45} \mu K^2 at
the 68% confidence level for l=151-693. Its likelihood function is asymmetric
and skewed positive such that with a uniform prior the probability of a
positive EE power is 96%. The powers of EB and BB signals at the 68% confidence
level are 18^{+27}_{-34} \mu K^2 and -31^{+31}_{-19} \mu K^2 respectively and
thus consistent with zero. The upper limit of the BB-mode at the 95% confidence
level is 9.5 \mu K. Results from the frequentist approach are in agreement
within statistical errors. These results are consistent with the current
concordance LCDM model.
