The Gemara in Masechet Shabbat (12) states that it is forbidden on Shabbat to read by the light of a candle. Before the advent of electric lights, people would use oil lamps for illumination. As the oil supply in the lamp would start to be depleted, the flame would flicker, and one would then tilt the lamp so the remaining oil would flow toward the wick, thereby producing a brighter, steadier flame. The Sages feared that if a person would read by the light of a candle on Shabbat, he might tilt the lamp as the light begins to flicker, which would violate the Torah prohibition of "Mabíir" (kindling). Especially when a person is focused on the material he is reading, he might instinctively tilt the lamp, forgetting that it is Shabbat, and Hazal therefore forbade reading by candlelight on Shabbat. This prohibition is codified by the Shulhan Aruch (Orah Haim 275:1).
This prohibition does not apply to electric lighting. Electric lights, unlike the light produced by oil lamps, do not fade or flicker. When the bulb burns out, the light turns off completely. Clearly, then, when it comes to electric lighting, there is no concern that one might perform a forbidden act to improve the light, and thus it is entirely permissible to read by an electric light on Shabbat.
However, Hacham Bension Abba Shaul (Israel, 1923-1998), in his work Or Leísion (vol. 2), makes an exception in the case of a light with a dimmer, a knob that can be turned to make the light brighter or more dim. Since one can turn the knob to make the light brighter, such a light resembles an oil lamp and is thus subject to the prohibition against reading by candlelight on Shabbat. However, Hacham Bension distinguishes in this regard between reading Torah material and reading other materials, and allows learning Torah by an electric light that has a dimmer. Since the light does not flicker, and remains steady, there is a basis for leniency, and therefore we may be lenient for the sake of Torah study. Other reading, however, is forbidden if the light has a dimmer.
Hacham Ovadia Yosef disagreed, and maintained that all reading is permitted, even if the light has a dimmer. He writes that Hazal enacted a prohibition relevant to oil lamps, and we do not have the authority to enact an additional prohibition relevant to electric lights. Hazalís enactment clearly did not relate to electric lights, which did not exist at that time, and we cannot institute our own edicts. Additionally, Hazalís concern was that one may tilt the lamp so the remaining oil would flow to the wick, but not that one might add more oil to the lamp. Turning the knob of a dimmer has the effect of allowing more electricity to flow to the lamp, which is akin to pouring more oil into the lamp, and Hazal never instituted a prohibition out of this concern. And, as mentioned earlier, the concern was because of a flickering light, which does not occur in the case of a dimmer. Therefore, reading is permissible by all electric lights, including lights with a dimmer.
However, one must remember that reading by candlelight is forbidden on Shabbat. Thus, for example, if the electric lighting in the dining room goes out, and the only light in the room is provided by the oil candles lit for Shabbat, one would not be allowed to read by the light of the candles.
Summary: It is forbidden to read by the light of oil candles on Shabbat, but it is permissible to read by electric lights, and there is no distinction in this regard between ordinary electric lights and lights with a dimmer.