The basic properties of stellar oscillations are reasonably well understood, allowing measurements of their frequencies to be used as probes of stellar interiors. The detailed understanding of the processes responsible for the oscillations, in the very broad range of stars observed to pulsate, has improved substantially over the past decade, as have the techniques for asteroseismic investigations on the basis of the observations. Here I provide a brief overview of the theory of stellar oscillations, emphasizing several cases of recent progress, often inspired by new observational developments.

The Local Group provides an interesting and representative sample of galaxies in the rest of the Universe. The high accuracy with which many problems can be addressed in Local Group galaxies is of paramount importance for understanding galaxy formation and evolution. This contribution presents a short review of overall Local Group properties followed by short discussions of five topics in which the study of Local Group members provides particularly significant information. These topics are only examples of the usefulness and potential of Local Group research. The five selected topics are the formation of the Milky Way, galaxy destruction and tidal streams, detailed galactic chemical evolution, star formation history determination, and low surface brightness extended structures.

The DIRECT project aims to determine direct distances to two important galaxies in the cosmological distance ladder – M31 and M33 – using detached eclipsing binaries (DEBs) and Cepheids. I summarize the results of the project and present some results from follow-up observations.

We investigate the influence of blending on the Cepheid distance scale using two Local Group galaxies, M31 and M33. Blending leads to systematically low distances to galaxies observed with the HST, and therefore to systematically high estimates of H0. High-resolution HST images are compared to our ground-based data, obtained as part of the DIRECT project, for a sample of 22 Cepheids in M31 and 102 Cepheids in M33. For a sample of 22 Cepheids in M31, the average (median) flux contribution from luminous companions not resolved on the ground-based images in the V-band, SV, is about 19% (12%) of the flux of the Cepheid. For 102 Cepheids in M33 the average (median) values of SV, SI, SB are 23% (13%), 28% (20%), 28% (15%). For 64 Cepheids in M33 with periods in excess of 10 days the average (median) SV, SI, SB are 16% (7%), 23% (12%), 20% (10%).

I present a brief analysis of K-band period-luminosity relations for AGB stars in the SMC based on OGLE, 2MASS and DENIS data. I also present, for a selected sample of SMC and LMC stars, a comparison between the analysis of respective MACHO and OGLE data and a method to combine the data from the two surveys.

We cross-correlated the OGLE-II database with the SIRIUS JHK survey data in the Large Magellanic Cloud (LMC). After eliminating obvious spurious variables, we determined the pulsation periods for 9 681 stars by applying the Phase Dispersion Minimization (PDM) technique to the OGLE-II data. Based on these data, we studied the period-K magnitude (PK) relations of variable stars in the LMC and found a new sequence. Comparison between the theoretical pulsation model (Wood & Sebo 1996) and observational data suggests that the variable stars on the new sequence are Mira variables pulsating in the first overtone mode.

We present a period analysis of more then 23 000 red giants in the Large Magellanic Cloud observed by the OGLE-II microlensing project. Periods combined with the single-epoch 2MASS J H KS magnitudes revealed the complex distributions of stars in the period-luminosity plane. Besides four different sequences corresponding to different modes of pulsation in AGB stars, we also discovered two distinct and well-separated sequences below the tip of the Red Giant Branch, consisting of almost 10000 short-period and low-amplitude red variable stars. We propose that the majority are likely to be first ascent red giants, showing radial pulsations in the second and third overtone modes.

We present an overview of our study of the short period variable stars in the Large Magellanic Cloud, and in the dwarf galaxies Fornax, Leo I, and NGC 6822. Light curves are presented for RR Lyrae stars, Anomalous Cepheids and, for the first time, for Dwarf Cepheids in the field and in the globular cluster #3 of the Fornax galaxy.

The MEGA microlensing survey is introduced and several topics about variable stars in M31 are discussed. An adopted model population of semiregular (SR) variable stars is presented, and the efficiency to recover these stars in M31 in a specific example MEGA dataset is predicted. The period-flux amplitude relation of the SRs discovered by MEGA could be used to measure the inclination of the M31 disk.

Dwarf galaxies in the local group provide a unique astrophysical laboratory. Despite their proximity some of these systems still lack reliable distance determinations as well as studies of their stellar content and star formation history. We present first results of our survey of variable stars in a sample of six local group dwarf irregular galaxies. Taking the Leo A dwarf galaxy as an example we describe observational strategies and data reduction. We discuss the light curves of two newly found Cepheids and place them into the context of a previously derived P-L relation. Finally we discuss the LPV content of Leo A.

We present results of the search for pulsating variable stars in the Magellanic Cloud fields covering central parts of these galaxies. The data were collected during the second phase of the Optical Gravitational Lensing Experiment survey (OGLE-II) from 1997 to 2000. In total, several thousand pulsating stars (Cepheids, RR Lyr) were found in both Magellanic Clouds. The photometric data of all objects are available to the astronomical community from the OGLE Internet archive. We present basic properties of pulsating stars in the Magellanic Clouds including Period–Luminosity relations for Cepheids. We also discuss observational prospects for the pulsating star field in the ongoing third phase of the OGLE project (OGLE-III) which started in 2001.

Recently we completed the VATT/Columbia survey monitoring a portion of M31 for microlensing and stellar variability, and report here on the microlensing result. Also, we have nearly completed a much larger survey (MEGA) covering most of the stars in M31, for which we have started cataloging many tens of thousands of Cepheids, Miras, eclipsing variables and other kinds of variable stars. The microlensing results from these two surveys hint that a significant fraction of the dark matter in M31 is composed of stellar-mass objects in the halo.

We present first results of an optical wide field imaging survey of the galaxies NGC 300, NGC 6822, WLM and Phoenix, performed as part of the Araucaria Project, a long-term observational program recently initiated at the Universidad de Concepción. Based on our data, a large number of new Cepheids in these galaxies has been found. Our photometric databases were also used to select blue supergiant candidates in these galaxies, and to search for the photometric variability of these stars, as well as for a number of side projects, such as the search of other types variable stars and OB associations in these galaxies.

Results are presented on a study of the short period variable stars in the dwarf irregular galaxy NGC 6822. We observed an almost uniformly populated classical instability strip from the Horizontal Branch up to the Classical Cepheid region. The main goal we achieved from the analysis of the faint sample is the first detection of RR Lyrae stars in this galaxy.

We have determined quasi-geometric distances to the Magellanic Clouds, M31 and M33. Our analysis uses a Bayesian statistical method to provide mathematically rigorous and objective solutions for individual Cepheids. We combine the individual distances with a hierarchical Bayesian model to determine the galactic distances. We obtain distance moduli 18.87 ± 0.07 mag (LMC, 12 stars), 19.14 ± 0.10 (SMC, 8 stars), 23.83 ± 0.35 mag (M33, 1 star) and 25.2 ± 0.6 mag (M31, 1 star) – all uncorrected for metallicity. The M31 and M33 distances are very preliminary. If the PL relations of the LMC, SMC and Galaxy are identical, our results exclude the metallicity effect in the V, (V – R) surface brightness method predicted by Hindsley & Bell (1989) at the 5σ level. Alternately, if Hindsley & Bell’s prediction is adopted as true, we find a metallicity effect intrinsic to the Cepheid PL relation requiring a correction Δ(V – Mv) = (0.36 ± 0.07)Δ[A/H] mag. The latter has the opposite sign to other observational estimates of the Cepheid metallicity effect.

Cepheid variable stars are fundamental to the calibration of the extragalactic distance scale. We present radial velocities, preliminary metallicities, and preliminary surface brightness distances of Cepheids in Local Group galaxies M31 and M33 using data obtained with the High Resolution Spectrograph on the Hobby-Eberly Telescope at McDonald Observatory. These data are the first step toward surface brightness distance measurements and metallicity calibrations of these extragalactic Cepheids.

The light curves of four recent fast LMC novae (Nova LMC 1988a, 1992, 1995, 2000) have been analysed to obtain the parameter t2 the time for a two magnitude decline below maximum light. Using the calibration of Della Valle & Livio (1995), values of MV at maximum are obtained. The weighted mean distance modulus to the LMC based on these novae is 18.89 ± 0.16. This differs significantly from the distance modulus adopted by Della Valle & Livio of 18.50, but only differs at the 1σ-level from Feast’s (1999) value of 18.70 ± 0.10. The evidence based on these novae suggests that either: (i) DMLMC = 18.50 is too close for the LMC; or (ii) some novae in the LMC, including these four, are significantly underluminous at maximum light compared with those in M31, by about 0.4 mag. This could be a metallicity effect, given that more metal-rich M31 novae were predominantly used by Della Valle & Livio to obtain their calibration.