Searching for 2D Superconductivity in La2−xSrxCuO4 Single Crystals Introduction Stiffnessometer a Magnetic Field Free Superconducting Stiffness Meter and Its Application The Nature of the Phase Transition in the Cuprates as Revealed by the Stffnessometer Opening a Nodal Gap by Fluctuating Spin Density Wave in Lightly Doped La2 xSrxCuO4 Conclusions A new experimental method – the Stiffnessometer is developed to measure elementary properties of a superconductor including the superconducting stiffness and the critical current. This technique has many advantages over existing methods such as: the ability to measure these properties while minimally disturbing the system; the ability to measure large penetration depths (comparable to sample size) as necessary when approaching the critical temperature; and the ability to measure critical currents without attaching contacts and heating the sample. The power of this method is demonstrated in a study of the penetration depth of LSCO where striking evidence is found for two separate critical temperatures for the in plane and out of plane directions. The results in the thesis are novel important and currently have no theoretical explanation. The stiffnessometer in a tool with great potential to explore new grounds in condensed matter physics