The capacity of the two-user Gaussian interference channel has been a long-standing open problem in information theory. This paper presents a simplified Han-Kobayashi scheme that achieves rates within one bit/s/Hz of the channel capacity for all values of the channel parameters. The scheme is asymptotically optimal in certain high SNR regimes. The paper also provides a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios. The paper analyzes the symmetric Gaussian interference channel, where both users have the same signal-to-noise ratio (SNR) and interference-to-noise ratio (INR). It shows that the symmetric capacity can be characterized in five different regimes based on the relationship between SNR and INR. In the weak interference regime, where the interference is not strong enough to be decoded in its entirety, the capacity is determined by the trade-off between decoding common and private information. In the strong interference regime, where the interference is strong enough to be decoded, the capacity is determined by the sum of the SNR and INR. The paper also derives new upper bounds on the capacity of the interference channel, which are tighter than previous bounds in certain parameter ranges. These bounds are used to show that the simple Han-Kobayashi scheme achieves rates within one bit/s/Hz of the capacity. The paper also defines generalized degrees of freedom for the symmetric interference channel, which quantify the reduction in channel capacity due to interference. The generalized degrees of freedom are shown to be a function of the ratio of INR to SNR in dB scale. The paper concludes that the simple Han-Kobayashi scheme is a powerful tool for achieving near-capacity performance in the Gaussian interference channel. The results provide a deeper understanding of the fundamental trade-offs between interference and capacity in wireless communication systems.The capacity of the two-user Gaussian interference channel has been a long-standing open problem in information theory. This paper presents a simplified Han-Kobayashi scheme that achieves rates within one bit/s/Hz of the channel capacity for all values of the channel parameters. The scheme is asymptotically optimal in certain high SNR regimes. The paper also provides a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios. The paper analyzes the symmetric Gaussian interference channel, where both users have the same signal-to-noise ratio (SNR) and interference-to-noise ratio (INR). It shows that the symmetric capacity can be characterized in five different regimes based on the relationship between SNR and INR. In the weak interference regime, where the interference is not strong enough to be decoded in its entirety, the capacity is determined by the trade-off between decoding common and private information. In the strong interference regime, where the interference is strong enough to be decoded, the capacity is determined by the sum of the SNR and INR. The paper also derives new upper bounds on the capacity of the interference channel, which are tighter than previous bounds in certain parameter ranges. These bounds are used to show that the simple Han-Kobayashi scheme achieves rates within one bit/s/Hz of the capacity. The paper also defines generalized degrees of freedom for the symmetric interference channel, which quantify the reduction in channel capacity due to interference. The generalized degrees of freedom are shown to be a function of the ratio of INR to SNR in dB scale. The paper concludes that the simple Han-Kobayashi scheme is a powerful tool for achieving near-capacity performance in the Gaussian interference channel. The results provide a deeper understanding of the fundamental trade-offs between interference and capacity in wireless communication systems.