We report a study of the ferromagnetism of ZrZn2, the most promising material to exhibit ferromagnetic quantum criticality, at low temperatures T as function of pressure p. We find that the ordered ferromagnetic moment disappears discontinuously at pc=16.5 kbar. Thus a tricritical point separates a line of first order ferromagnetic transitions from second order (continuous) transitions at higher temperature. We also identify two lines of transitions of the magnetisation isotherms up to 12 T in the p − T plane where the derivative of the magnetization changes rapidly. These quantum phase transitions (QPT) establish a high sensitivity to local minima in the free energy in ZrZn2, thus strongly suggesting that QPT in itinerant ferromagnets are always first order.PACS numbers: 71.27.+a, 75.50.Cc, 74.70.Tx The transition of a ferromagnet to a paramagnet with increasing temperature is regarded as a canonical example of a continuous (second order) phase transition. This type of behavior has been well established in many materials ranging from nickel [1] to chromium tribromide [2]. The detailed variation of the order parameter near the critical point, in this case the Curie temperature, has been analyzed in a wide variety of systems using classical statistical-mechanical models for the case when the Curie temperature is not too small. Classical statistics are appropriate when all fluctuating modes have energies much less than k B T c . It was pointed out by Hertz [3] that the system undergoes a 'quantum' phase transition (QPT) when the transition is driven by non-thermal fluctuations whose statistics are in the quantum limit.The search for a second order (critical) QPT in itinerant electron systems, which are believed to be responsible for enigmatic quantum phases like magnetically mediated superconductivity and non-Fermi liquid behavior, has become of particular interest in recent years. Experimental studies have thereby revealed notable differences from "standard" second order behaviour in all materials investigated to date. For example, in MnSi [4] and UGe 2 [5], itinerant-electron magnetism disappears at a first order transition as pressure is applied. The bilayer ruthenate Sr 3 Ru 2 O 7 , undergoes a field induced QPT with multiple first-order metamagnetic transitions [6] and associated non-Fermi liquid behavior in the resistivity [7]. However, these materials have complicating factors: the zero-field ground state of MnSi is a helical spin spiral; UGe 2 is a strongly uniaxial (Ising) system; Sr 3 Ru 2 O 7 is a strongly two-dimensional metal. In fact, theoretical studies suggest [8, 9, 10, 11] that ferromagnetic transitions in clean three-dimensional (3D) itinerant ferromagnets at T = 0 are always first order.In this Letter we address the nature of the ferromagnetic QPT experimentally. The system we have chosen is the itinerant ferromagnet ZrZn 2 , which is a straight forward itinerant ferromagnet with a cubic (C15) structure and small magnetic anisotropy. ZrZn 2 has a small ordered moment (M = 0.17µ B f.u. −1 ...