We present multiple spectropolarimetric observations of the nearby Type Ia supernova (SN) 2011fe in M101, obtained before, during, and after the time of maximum apparent visual brightness. The excellent time coverage of our spectropolarimetry has allowed better monitoring of the evolution of polarization features than is typical, which has allowed us new insight into the nature of normal SNe Ia. SN 2011fe exhibits time-dependent polarization in both the continuum and strong absorption lines. At early epochs, red wavelengths exhibit a degree of continuum polarization of up to 0.4%, likely indicative of a mild asymmetry in the electron-scattering photosphere. This behavior is more common in sub-luminous SNe Ia than in normal events, such as SN2011fe. The degree of polarization across a collection of absorption lines varies dramatically from epoch to epoch. During the earliest epoch a $lambda$4600-5000 AA complex of absorption lines shows enhanced polarization at a different position angle than the continuum. We explore the origin of these features, presenting a few possible interpretations, without arriving at a single favored ion. During two epochs near maximum, the dominant polarization feature is associated with the Si{sc ii} $lambda$6355 AA absorption line. This is common for SNeIa, but for SN2011fe the polarization of this feature increases after maximum light, whereas for other SNeIa, that polarization feature was strongest before maximum light.