  In this work we present the most comprehensive INTEGRAL AGN sample which
lists 272 objects. Here we mainly use this sample to study the absorption
properties of active galaxies, to probe new AGN classes and to test the AGN
unification scheme. We find that half (48%) of the sample is absorbed while the
fraction of Compton thick AGN is small (~7%). In line with our previous
analysis, we have however shown that when the bias towards heavily absorbed
objects which are lost if weak and at large distance is removed, as it is
possible in the local Universe, the above fractions increase to become 80% and
17%. We also find that absorption is a function of source luminosity, which
implies some evolution in the obscuration properties of AGN. Few peculiar
classes, so far poorly studied in the hard X-ray band, have been detected and
studied for the first time such as 5 XBONG, 5 type 2 QSOs and 11 LINERs. In
terms of optical classification, our sample contains 57% of type 1 and 43% of
type 2 AGN; this subdivision is similar to that found in X-rays if unabsorbed
versus absorbed objects are considered, suggesting that the match between
optical and X-ray classification is overall good. Only a small percentage of
sources (12%) does not fulfill the expectation of the unified theory as we find
22 type 1 AGN which are absorbed and 10 type 2 AGN which are unabsorbed.
Studying in depth these outliers we found that most of the absorbed type 1 AGN
have X-ray spectra characterized by either complex or warm/ionized absorption
more likely due to ionized gas located in an accretion disk wind or in the
biconical structure associated to the central nucleus, therefore unrelated to
the toroidal structure. Among 10 type 2 AGN which resulted to be unabsorbed, at
most 3-4% is still eligible to be classified as a "true" type 2 AGN.
