Final Activity Report Summary - HIGGS AT CDF (Constraining the Higgs boson with the CDF experiment at the Tevatron) Our present knowledge of the fundamental building blocks of matter and their interactions are summarised in the Standard Model of particle physics. In the Standard Model one distinguishes between fermions (quarks and leptons) which form observable matter and the bosons (photons, gluons, W and Z) which are responsible for their interactions (forces). A key component of the Standard Model is spontaneous electroweak symmetry breaking, which gives rise to the mass of all fermions and the W and Z bosons. The only resulting physical manifestation of this process is a new particle, the Higgs boson, whose exact mass is unspecified. Without the Higgs boson the Standard Model would require all the other particles to be massless, in contradiction to the data.The Higgs boson is the only particle predicted by the highly successful Standard Model which has yet to be found experimentally. The discovery of this last missing particle is of utmost importance for particle physics as it will allow for a full test of the Standard Model, and give an answer to the origin of mass. There are two important steps towards an eventual discovery of the Higgs boson. First, measurements have to constrain the allowed mass of the Higgs boson. This is possible through the effects of radiative quantum corrections on the properties (such as their mass) of other particles. Through the electroweak radiative corrections it is possible to infer a constraint on the allowed mass, thus helping the actual discovery. The mass of the W boson receives sizeable quantum correction from the Higgs boson and the top quark. Since the top quark mass has been measured precisely, a precise measurement of the W boson mass can be used to constrain the mass of the yet unobserved Higgs boson. We measured the W boson mass to be MW=80.413+-0.048 MeV/c2. With a total uncertainty of 0.06%, this represents the single most precise W boson mass measurement to date. The updated Higgs boson mass constraint is MH = 76(+33)(-24) GeV/c2.The second step consists of direct searches for the Higgs boson. The relatively low mass favours a detection channel, where a Higgs boson is produced together with a W boson. This is a particularly difficult channel that suffers from large backgrounds. There is one important and exciting intermediate step. Top quarks can be produced not only in pairs (as they were discovered in 1995) but also singly through an electroweak vertex. Observation of this new particle state is an important milestone to an eventual Higgs discovery. We detected evidence for this process with a signal significance of 3.1 standard deviations. This proves the viability of the method. However since the production probability of Higgs bosons is an order of magnitude smaller compared to singly produced top quarks, more data is needed. Initial studies suggest that evidence for a Higgs signal can be established by combining many decay channels and using the full Tevatron dataset, expected to be available in 2-3 years.