Toshikazu Onishi Title:Star Formation in the Large Magellanic Cloud: Tracing an Evolution of Giant Molecular Clouds Abstract: Most stars are born as clusters in Giant Molecular Clouds (hereafter GMCs), and therefore the understanding of the evolution of GMCs in a galaxy is one of the key issues to investigate the evolution of the galaxy. Recent high spatial resolution observations enable us to reveal the distribution of GMCs in the nearby galaxies and the physical properties, and the evolution leading to cluster formations are actively being investigated. Some of the merits of the GMC study in an external galaxy are that we can study the physical properties of the samples with the same spatial resolutions across a wide range of environments throughout a galaxy and that we can easily identify associations of various kinds of objects if the galaxy is nearly face-on. The LMC is the nearest star-forming galaxy (distance ~ 50kpc) and is almost face-on. From these aspects, it is becoming the most popular region for studying interstellar medium over an entire galaxy. For molecular gas, the NANTEN covered the entire LMC with a spatial resolution of 40 pc, revealing 272 molecular clouds whose mass ranges from ~10^4 to ~10^7 solar masses, which is the first uniform sample of GMCs in a single galaxy. Comparison with HII regions and young clusters revealed the evolutional sequence of GMCs from starless stage to the massive star forming stage, and finally to dispersal of GMCs due to the effect of the explosive events. The uniform physical resolution and sensitivity allowed constraint of molecular cloud lifetimes and evolution. Following observations in the lines of J=1-0, 2-1, 3-2, 4-3, and 7-6 lines of 12CO and 13CO revealed the detailed physical properties of the molecular gas with a spatial resolution of ~5pc, and then hot and dense molecular clumps are detected toward HII regions. Our Spitzer SAGE and Herschel HERITAGE surveys show that the interstellar medium has much smaller scale structures; full of filamentary and shell-like structures. In order to resolve the filamentary distributions and pre-stellar cores we definitely need to resolve clouds at sub-pc resolutions with ALMA and to cover regions of active cluster formation which are to be selected based on the Spitzer and Hershel data. Our ALMA targets in Cycle 1 include N159, which is the most intense and concentrated molecular cloud as shown by the brightest CO J=3-2 source in the LMC, and GMCs with different evolutionary stages. We present the first maps of pre- stellar cores and linking filaments at sub-pc resolution and discuss the formation process of massive clusters.