  In this paper we present a construction of the compact form of the
exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We
realize F4 as the automorphisms group of the exceptional Jordan algebra, whose
elements are 3 x 3 hermitian matrices with octonionic entries. We use a
parametrization which generalizes the Euler angles for SU(2) and is based on
the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us
to determine an explicit expression for the Haar invariant measure on the F4
group manifold. Apart from shedding light on the structure of F4 and its coset
manifold OP2=F4/Spin(9), the octonionic projective plane, these results are a
prerequisite for the study of E6, of which F4 is a (maximal) subgroup.
