We present the results of the analysis of FLS 1718+59, a galaxy-galaxy gravitational lens system in the Spitzer First Look Survey (FLS) field. A background galaxy (zs = 0.245) is severely distorted by a nearby elliptical galaxy (zl = 0.08), via gravitational lensing. The system is analysed by several methods, including surface brightness fitting, gravitational lens modeling, and spectral energy distribution fitting. From Galfit and Ellipse we measure basic parameters of the galaxy, such as the effective radius and the average surface brightness within it. gravlens yields the total mass inside the Einstein radius (REin), and MAGPHYS gives us an estimate of the stellar mass inside REin. By comparing these parameters, we confirm that the lens galaxy is an elliptical galaxy on the Fundamental Plane and calculate the stellar mass fraction inside REin, and discuss the results with regards to the initial mass function.

We now have more than 70 multiple image gravitational lens systems. Since gravitational lensing occurs through gravitational distortions in cosmic space, cosmological informations can be extracted from multiple image systems. Specifically, Hubble constant can be determined by the time delay mea-surement, curvature of the universe can be measured by the distribution of image separations in lens systems, and limits on matter density and cosmological constant can be set by the statistics of gravitationallens systems. Uncertainties, however, still exist in various steps, and results may be taken with some caution. Larger systematic survey and better understanding of galaxy properties would definitely help.

When a bright astronomical object (source) is gravitationally lensed by a foreground mass (lens), its image appears to be located at different positions. The lens equation describes the relations between the locations of the lens, source, and images. The lens equation used for the description of the lensing behavior caused by a lens system composed of multiple masses has a form with a linear combination of the individual single lens equations. In this paper, we examine the validity of the linear nature of the multi-lens equation based on the general relativistic point of view.

It is shown in this paper that the astigmatic property of single gravitational lens in static bounded gravitational field can be retained, if n-gravitating body as a whole acts simultaneously as gravitational lens.

The transverse velocities of the gravitational lens system (galaxy plus a 'disturbing star') and their dependences on unkown properties of the source and the deflecting object are discussed. We have derived an analytic expression for the transverse velocity in terms of the velocities of the light source, the gravitational lensing galaxy and the 'disturbing star', and the observer. The results are then further applied to an estimate of the expectation value of the absolute transverse velocity and of the probable time scales of flux changes of the double QSO 0957+561A, B.