Most stars change little in outward appearance for more than 90 percent of their lifetime. A star like the Sun, for example, will remain roughly the same for 10 billion years before it runs out of fuel and eventually dies. Most stars are destined to end their lives quiescently, their outer layers escaping into interstellar space. But some die violently in spectacular explosions, called Supernovae (SNe), of almost unimaginable fury, enriching our Galaxy with newly created elements. The total amount of energy radiated by a supernova during the few months it takes to brighten and fade away, is roughly the same as the Sun will radiate during its entire 10¹⁰ year lifetime (10⁵¹ ergs).

     We have evidence that Supernovae occur in all galaxies, also in our own. Occasionally, they have been visible from Earth by naked eye, such as the Supernova of 1604, the 4th centennial of which will be celebrated on 2004, and that was observed by Galileo in Padua. In some cases, we can detect their glowing remains, or Supernova Remnants, for centuries or even millennia like in the case of the explosion in the year A.D. 1054 which gave birth to the famous Crab Nebula. From the point of view of life on Earth, probably the most important aspect of Supernovae is their role in creating, and then dispersing, the heavy elements out which both our planet and our bodies are made such as iron, silicon, copper, lead.

     The study of Supernovae is developing very rapidly thanks to new instruments, new interpretation and theoretical models. Supernovae are key actors in many fields of astrophysical research from Stellar to Galaxy Evolution, from the Physics of Compact Remnants to Cosmology. This wide interest explains why the discovery rate of new SNe has grown from about two SNe per month 20 years ago to almost one per day nowadays. Also the volume of Universe which is sampled with modern facilities has increased dramatically from nearby galaxies (look back time ~ 0) to deep surveys for high redshift objects (look back time >> several billions of years).

     Along with the increased number of objects, the improved detail in the study of SNe has led to a breakdown of our old classification scheme. Understanding the physics of these different kinds of explosions is a challenge, despite the fact that the source of energy needed to drive such powerful outbursts, i.e. gravitational binding and/or thermonuclear burning, has been known from decades.

     It is widely accepted that most massive stars explode due to core collapse. Yet the observed outcomes, and nucleosynthesis yields, depend on many factors that are still poorly constrained. In this respect we recall the rapid improvement in our knowledge that followed the discovery of a blue supergiant progenitor for SN1987A rather than a red supergiant, as expected. The ability of the HST to image the evolution of the remnant of SN1987A and the interaction of its shock with the nearby circumstellar medium, in particular the inner optical ring, is contributing greatly to our understanding of these phenomena. All of this is aided by new data covering the entire wavelength range from radio to X-ray and new theoretical interpretation of these results.

     While the massive stars are in general expected to retain their outer layers untill the explosion, in some cases they can loose all the H envelope, and in many cases even the He envelope, due to very strong mass loss, ending up as SN Ib or SN Ic. This apparently simple scenario has been complicated by the discovery of two new types of core collapse events. On one side there are underenergetic SNII, whose faint luminosity is attributed to the fall back of the inner ejecta material, mostrly radioactive ⁵⁶Ni, onto the newly formed collapsed remnant that likely turns into a black hole. At the other extreme are hypernovae, core collapse SNe which exhibit very high explosion energies and eject a mass of Fe-peak elements similar to that of SN Ia. They are especially interesting because at least two of them, SNe 1998bw and 2003dh, are associated with GRB events and constitute the possible ``missing link'' between SNe and GRBs.

     Despite the great importance of core collapse SNe, it has to be acknowledged that, in the last few years, most of the scene was dominated by the thermonuclear SN Ia. In particular, the study of very distant SNIa has impacted Cosmology by yielding an intriguing and puzzling picture of the Universe in which we live: apparently it is Euclidean, rather than curved as expected by many, but it seems to be not only open, and thus expanding forever, but expanding at an accelerating rate due to the presence of a so-called Dark Energy.

     While the importance of these results cannot be overemphasized, they do rest on a number of assumptions and on a not-fully-understood physics of the explosion and nature of the progenitors. The major efforts dedicated in the last decade to the observations of SN Ia for their use as cosmological probes, have demonstrated the significant dispersion of the absolute luminosities that seems to require that the Ni yields in different events range between 0.1 to 1.0 M_o. In the favoured scenario the explosion occurs when the progenitor reaches the Chandrasekhar mass (1.4 M_o). A well-known problem of this scenario concerns the configuration of the progenitor systems; two different models have been proposed: the so called single degenerate scenario (SD), i.e. H-rich matter accreted onto the WD that is burned firstly into He and then into C-O, and the double degenerate scenario (DD), i.e. two CO WDs merging on a timescale smaller than the Hubble time. Alternatively, it has been suggested that faint SN Ia originate from sub-Chandrasekhar mass progenitors with a total mass as low as 0.7 M_o. In all cases it is not yet clear what is the driving mechanism for the realization of the different events. One important clue is that faint SN Ia seem to occur preferentially in early type galaxies which makes a link with the age or possibly with the metallicity of the parent stellar population.

     Even though significant progress has been made in recent years, many of the properties of SNe remain largely uncertain. This motivated the organisation of the several large international collaborations with the aim to achieve a better understanding of the physics of SNe at both low and high redshifts.
It becomes important at this point to have new opportunities to confront the most recent results and give to young and expert researchers a broad-spectrum overview of the advances in the field.

     The organization of the Padua conference was born from this demand.