Here we report a study of vortex states in a thin superconducting film with a magnetic dot grown upon it by means of a method based on London-Maxwell equations. Vortices with single quantum flux (Φ0 = hc/2e), giant vortices ( vortices with multiple flux ) as well as antivortices ( vortices with negative vorticity ) are taken into consideration. It turns out that giant vortices occur, when the dot's size is sufficiently smaller ( R ≤ 4.5ξ) than the effective penetration depth Λ. In the case of a dot with sufficiently large size ( R ≥ 6ξ ), the vortices with single quantum flux dominate the vortex states. Their geometrical patterns are predicted up to seven vortices. Our calculations do not show the spontaneous appearance of antivortices. PACS Number(s): 74.25. Dw, 74.25.Ha, 74.25.Qt, Type II superconductors are used in a wide variety of technological applications due to their high critical currents and fields [1]. In these superconductors, vortices appear when the magnetic field exceeds the first critical field H c1 . Under external current or field, vortices move, which causes the superconductor to switch to a resistive state. As a result, the system loses its superconductivity. Because of this, vortex pinning is quite important in applications of type II superconductors. One of the ways to pin vortices is to use the magnetic subsytems with either out-of-plane or in-plane magnetization. These subsystems are capable of trapping both vortices and antivortices, depending on the orientation and strength of their magnetization. The aforementioned systems are not only important for technological applications, such as devices that can be tuned by weak magnetic fields, but also offer rich physical effects which are not observed in the individual parts. Some of these effects were predicted elsewhere [2][3][4][5][6][7].In the recent decade, magnetic dots growing on top of SC films have been extensively studied both experimentally [8] and theoretically [9,10]. In experimental studies, magnetic dots with in-plane magnetization are fabricated from Co, Ni, Fe, Gd-Co and Sm-Co alloys, whereas, for the dots with magnetization perpendicular to the plane, Co/Pt multilayers are used [11]. These studies report commensurability effects on transport properties, which comfirm that the dots create and pin vortices. On theoretical side, several realizations of the aforementioned systems are analyzed through the Landau-Gizburg framework and London theory. In these works, the authors investigated the conditions for vortices to appear and calculated their geometric configurations in equilibrium.Recently, Priour et al. studied the vortex states of a SC film with a magnetic dot array grown upon on it, through Ginzburg-Landau theory, and found several different configurations of vortices in the SC film [12]. Similar study was also done by Peeters et al., but in the presence of a single dot [13,14]. One of the interesting results that is reported by these works is, when the dot's size is on the order of a few coherence lengths ξ, vortices with...