This paper proposes methodologies for statistical inference of low-dimensional parameters in high-dimensional linear models. The focus is on constructing confidence intervals for individual coefficients and linear combinations of several coefficients in a linear regression model. The theoretical results provide sufficient conditions for the asymptotic normality of the proposed estimators and a consistent estimator for their finite-dimensional covariance matrices. These conditions allow the number of variables to far exceed the sample size. The simulation results demonstrate the accuracy of the coverage probability of the proposed confidence intervals, supporting the theoretical findings. The methodology involves a low-dimensional projection (LDP) approach, which does not require the uniform signal strength condition, a common requirement in variable selection consistency theory. The LDP approach is particularly useful when there are many potentially nonzero coefficients of small or moderate magnitude. The paper also discusses the use of LDP confidence intervals with multiplicity adjustment, providing more information about unknown regression coefficients compared to variable selection alone. The theoretical work justifies the use of LDP confidence intervals for preconceived parameters and simultaneous confidence intervals for all parameters. The main difference between the proposed LDP and existing variable selection approaches is the requirement of the uniform signal strength condition. The LDP approach is more practical, especially when the uniform signal strength condition fails to hold, as it can correctly select variables with small or moderate nonzero coefficients. The methodology is based on a relaxed orthogonalization of the design matrix and a bias-corrected linear estimator. The paper provides specific implementations, including the use of the scaled Lasso and the least squares estimator in the model selected by the scaled Lasso. The theoretical results are supported by simulation experiments and random matrix theory, ensuring the validity of the proposed methods under proper conditions.This paper proposes methodologies for statistical inference of low-dimensional parameters in high-dimensional linear models. The focus is on constructing confidence intervals for individual coefficients and linear combinations of several coefficients in a linear regression model. The theoretical results provide sufficient conditions for the asymptotic normality of the proposed estimators and a consistent estimator for their finite-dimensional covariance matrices. These conditions allow the number of variables to far exceed the sample size. The simulation results demonstrate the accuracy of the coverage probability of the proposed confidence intervals, supporting the theoretical findings. The methodology involves a low-dimensional projection (LDP) approach, which does not require the uniform signal strength condition, a common requirement in variable selection consistency theory. The LDP approach is particularly useful when there are many potentially nonzero coefficients of small or moderate magnitude. The paper also discusses the use of LDP confidence intervals with multiplicity adjustment, providing more information about unknown regression coefficients compared to variable selection alone. The theoretical work justifies the use of LDP confidence intervals for preconceived parameters and simultaneous confidence intervals for all parameters. The main difference between the proposed LDP and existing variable selection approaches is the requirement of the uniform signal strength condition. The LDP approach is more practical, especially when the uniform signal strength condition fails to hold, as it can correctly select variables with small or moderate nonzero coefficients. The methodology is based on a relaxed orthogonalization of the design matrix and a bias-corrected linear estimator. The paper provides specific implementations, including the use of the scaled Lasso and the least squares estimator in the model selected by the scaled Lasso. The theoretical results are supported by simulation experiments and random matrix theory, ensuring the validity of the proposed methods under proper conditions.