The study will consist of 2 phases, a Phase I or dose escalation phase and a Phase II or expansion phase. Paediatric/young adult patients with relapsed or refractory B cell ALL will be enrolled. Eligible patients will undergo leukapheresis in order to harvest T cells, which is the starting material for the manufacture. Autologous CAR T product directed against CD19-expressing tumor cells (CD19-CART01) will be produced and, after a lymphodepletion with conventional chemoterapic agents, the patient will receive CD19-CART01 intravenously. The construct contains also the suicide gene safety switch "inducible Caspase 9"; therefore, in case of relevant toxicities, the patient will receive the dimerizing agent in order to induce the apoptosis of the cells.