Introduction.- 1 Preliminary facts on semi-boundedness of forms and operators.- 2 Lp-dissipativity of scalar second order operators with complex coefficients.- 3 Elasticity system.- 4 Lp-dissipativity for systems of partial differential operators.- 5 The angle of Lp-dissipativity.- 6 Higher order differential operators in Lp.- 7 Weighted positivity and other related results.- References.